ž *The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for
the Ultimate Theory *by Brian Greene

ž *The Theoretical Minimum: What You Need to Know to Start Doing Physics *by Leonard Susskind and
George Hrabovsky

ž *The Road to Reality: A Complete Guide to the Laws of the Universe* by Roger Penrose

ž *A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to
the Mathematics of Relativity *by Peter Collier

ž *The Character of Physical Law* by Richard Feynman

ž *QED: The Strange Theory of Light and Matter *by Richard Feynman

ž *Feynman¡¯s Lost Lecture: The Motion of Planets around the Sun*

ž *Why String Theory? *by Joseph Conlon

__Comments__: I got *The **Elegant Universe* as a birthday present,
and it is the best birthday present I have ever received.* The Theoretical Minimum *is similar to my homepage in purpose. This
series was written in mind for laymen who wish to learn real physics that is
not usually covered in popular physics books, but do not have access to
professors to ask questions as physics students do have. It is suitable for
self-study. However, the philosophy is somewhat different from my homepage. As
the title suggests, it covers the theoretical minimum a theoretical physicist
needs to know whereas my homepage covers way beyond the minimum as I believe
that it helps to be ¡°well-rounded.¡± *The
Road to Reality* is similar to my homepage in purpose. Beginning with basic
mathematical concepts such as complex numbers and logarithms, Penrose explains
all the mathematics needed to review advanced physics topics such as quantum
mechanics, general relativity, quantum field theory, string theory, loop
quantum gravity, and twistor theory. Therefore, the book is very long at over
1000 pages, but relatively cheap compared to its length. I think it would be a
good supplement to my homepage, especially the early chapters on mathematics.
These chapters cover some materials not covered on my homepage, and they
explain some of my covered materials in further detail. However, complaining
that ¡°the mathematical jargon was so intense¡± a reviewer at Amazon.com
cautions, ¡°the author had lost sight of the exact state of knowledge that the reader
would have achieved.¡± *A Most
Incomprehensible Thing* is a superb book on special relativity and general
relativity. As calculus and Newtonian mechanics are prerequisites to special
relativity and general relativity, it covers these topics concisely but
solidly. Feynman, a Nobel laureate in physics, was a great teacher, which is
exemplified in the next three listed books. Among these three, *The Character of Physical Law* is my
personal favorite. QED (i.e., quantum electrodynamics) was what Feynman got his
Nobel Prize for, and *QED: The Strange
Theory of Light and Matter *is his own explanation aimed at laymen. *Feynman¡¯s Lost Lecture: The Motion of
Planets around the Sun* is about Newton¡¯s geometric proofs on orbits of
planets around the sun, and it can be very difficult despite assuming only a
basic knowledge of mathematics. One can really appreciate that Newton was a
genius since he succeeded in the difficult proof that the orbit of a planet
should be an ellipse. Conlon explains what string theory is and why he works on
it in his book *Why String Theory?*. He
dedicated this book ¡°to the citizens and taxpayers of the United Kingdom¡± ¡°to
give back to those who have given to [him].¡±

**Popular physics
history-related books**

ž
*Surely, You¡¯re Joking Mr.
Feynman! (Adventures of a Curious Character)* by Richard Feynman.

ž
*A Passion for Discovery* by Peter Freund

ž
*The Recollections of *

ž
*Physics and Beyond,
Encounters and Conversations* by Werner Heisenberg

ž
*Schr**ö**dinger: Life and Thought* by Walter Moore

__Comments__: *Surely,
You¡¯re Joking Mr. Feynman!* is an autobiographical book by the late Feynman,
a Nobel laureate in physics. However, it¡¯s more of a collection of interesting
anecdotes than a serious genuine autobiography. As the author of *A Passion for Discovery *writes about his
own book, this book is comprised of ¡°more than 150 anecdotes, vignettes and
stories.¡± This book hardly talks about any physics, but it talks amply about
physicists. This book reminds us that physics, despite its divine origin, was
discovered by human beings like you and me. The late Wigner was a Nobel
laureate in physics, and *The
Recollections of Eugene. P. Wigner *is his autobiography, in which he hardly
talks about physics and instead focuses mostly on life lessons. *Physics and Beyond, Encounters and
Conversations *is an autobiography of Heisenberg, one of the founders of
quantum mechanics. It was selected as one of the one hundred books recommended
by Seoul National University. However, as much of the book is concerned with
Heisenberg¡¯s philosophical discussions with other people, I found it
occasionally hard to understand. *Schr**ö**dinger: Life and Thought* can be very technical
with a lot of mathematical formulas, but it is still interesting to learn about
Schrödinger, another one of the
founders of quantum mechanics.

**Popular math books**

ž *Who is Fourier? A Mathematical Adventure* by Transnational College of LEX

ž *Number: The Language of Science *by Tobias Dantzig

__Comments__: *Who is
Fourier? *is a book on Fourier transformation aimed at laymen. The Fourier
transformation is essential in physics, especially in quantum mechanics. As
trigonometric functions, complex numbers, vectors, and calculus are
prerequisites to understanding Fourier transformation, it does cover the very
basics, and with considerable success. Contrary to what the title
suggests, *Number: The Language of Science* does not actually deal with how
mathematics is used in science, but how the concept of number developed.
Einstein wrote, ¡°This is beyond doubt the most interesting book on the
evolution of mathematics which has ever fallen into my hands.¡± However, it
seems that there were some problems with editing. In the most recent edition
(2007) there were serious typos and omission of a figure.

**Physics history book
(technical)**

ž *Subtle is the Lord: The Science and the Life of Albert Einstein* by Abraham Pais

ž
*Inward Bound: Of Matter
and Forces in the Physical World* by Abraham Pais .

ž
*The Historical Development
of Quantum Theory, Vol 1~6 *by Jagdish Mehra and Helmet Rechenberg

ž
*The Story of Spin *by Sin-itiro Tomonaga

ž *QED and the Men Who Made It *by Silvan

ž
*Einstein¡¯s Unification* by Jeroen van Dongen* *

ž
*The Supersymmetric World:
The Beginnings of the Theory *by Gordon L. Kane and Mihail A. Shifman

ž
*The Birth of String Theory* by Dr. Andrea Cappelli,
Elena Castellani, Filippo Colomo and Paolo Di Vecchia

ž
*A Brief History of String
Theory: From Dual Models to M-Theory *by Dean Rickles

__Comments__: *Subtle is the Lord* is the best scientific biography of Albert
Einstein. *Inward Bound* is a history
book on twentieth-century particle physics. *The
Historical Development of Quantum Theory* is an excellent and very detailed
book on the history of quantum mechanics, even though you may find it long and
expensive. *The Story of Spin* was
written by the Japanese Nobel laureate Tomonaga, and provides interesting
stories such as how Pauli came to introduce spin and Pauli¡¯s exclusion
principle and how Heisenberg introduced isospin. In particular, if you are a
physics major, you don¡¯t have much opportunity to learn how Pauli first
introduced spin and Pauli¡¯s exclusion principle, as their details are included
neither in standard physics curriculum nor in any other ordinary physics
history books, because they perhaps should be considered now as chemistry
history. Also you will enjoy this book, if you just started to learn some basic
ideas of quantum field theory, such as the second quantization and the Dirac
equation. *QED and the Men Who Made It *is
a thick book that covers the history of quantum electrodynamics (QED) and the
four physicists, who made it. Three of the four physicists won the Nobel Prize
in 1965. Dyson, who showed that the methods of the three physicists were
equivalent, didn¡¯t. At a technical level, *Einstein's
Unification* deals with a lot of interesting topics, such as Einstein's
efforts and mistakes encountered upon constructing general relativity,
Einstein's methodological schema from which one can glimpse his epistemological
viewpoint, and Einstein's unified field theory with other collaborators. All
the books listed above require a solid knowledge of physics.

**Calculus**

ž *What **is Mathematics? An Elementary Approach to Ideas and Methods *by Courant, Robbins, and
Stewart

ž *Calculus **and Analytic Geometry* by Thomas and Finney

ž *Calculus:*
*Multivariable* by Anton, Bivens, Davis

__Comments__: *What is Mathematics?* is not a book on calculus per se, but it does cover
calculus. Einstein called the book ¡°A lucid representation of the fundamental
concepts and methods of the whole field of mathematics¡¦Easily understandable.¡±
Those eager to study calculus as soon as possible may skip the earlier chapters
and jump ahead to chapter VIII after reading only chapter VI which deals with
the concept of limit, an important prerequisite for calculus. *Calculus and Analytic Geometry* is a
suitable book from which to learn single variable calculus, though it covers a
little bit of multivariable calculus as well. *Calculus: Multivariable* is a suitable book from which to learn
multivariable calculus. Single variable calculus is a prerequisite to
multivariable calculus. Most science and engineering students learn
multivariable calculus in their first semester of freshman year.

**Linear Algebra**

ž *Vector **Calculus, Linear Algebra and Differential Forms: A Unified Approach *by Hubbard

ž *Linear** Algebra *by
Serge Lang

__Comments__: Frankly speaking, I do not
actually know which book is good for studying linear algebra. But the book by
Hubbard was a textbook for my honors class which covered multivariable
calculus, linear algebra, real analysis, differential forms and de Rham
cohomology in two semesters. I want to recommend this book only to students who
prefer absolute rigor of mathematical language to easy-going manners of verbal
explanation. I also want to note that the concept of differential forms is very
important to string theory, even though it can be easily learned in other
textbooks as well. The book by Serge Lang was recommended by a professor who
specializes in string theory, but it may be too abstract for beginners as it
uses very mathematical language. Maybe you can find a good non-mathematical book
with ample examples and calculations at Amazon.com by searching one with high
ratings. Most science and engineering students learn linear algebra in their
second semester of freshman year.

**General Physics (1st-year physics)**

ž *Fundamentals** of Physics* by
Halliday, Resnick, and Walker

ž *The **Feynman Lectures on Physics Volume I, II, III* by Feynman

__Comments__: *Fundamentals
of Physics* is the book that I used when I first learned college-level
physics. I loved this book, as every chapter starts out with a page that
includes a picture and an intriguing and meaningful question. After studying
each chapter, you can naturally answer the question. Also, the book contains
many interesting articles related to physics - for example, the physics of
ballet, the physics of transportation, and so on. The series by Feynman is more
difficult. Actually, it was used as a physics course at Caltech, but after two
years it was found that only a handful of students could follow it. I never
studied volume III, which treats quantum mechanics, but I studied volumes I and
II, and they were superb. In particular, volume II includes a wealth of
important material not usually treated in freshman-year physics; for example,
the angular momentum of electromagnetic fields, electric filters, and discussion
of 4-vector.

**Mechanics **

ž *Analytical **Mechanics*
by Cassiday and Fowles

ž *Classical** Mechanics*
by Goldstein*
*

__Comments__: Multivariable calculus is a prerequisite to
mechanics. *Analytical Mechanics* is
suitable for undergraduate sophomores who have studied freshman physics. This
book does a great job explaining concepts, and I met with no hardship studying
it on my own. *Classical Mechanics* is
usually used as a graduate-level textbook. Studying the first without the
second is sufficient preparation for higher-level courses such as quantum
mechanics and general relativity.

**Electromagnetism**

ž *No-Nonsense
Electrodynamics: A Student-Friendly Introduction*
by Schwichtenberg

ž *Electricity and Magnetism* (*Berkeley
Physics Course*) by Purcell

ž *Introduction to Electrodynamics* by Griffiths

__Comments__: All of these three books are very well-written
and easy to follow. As the author says, *No-Nonsense
Electrodynamics* ¡°focuses solely on the fundamental aspects of
Electrodynamics.¡± Most other electrodynamics books spend vast amount of pages
to cover how to solve Maxwell¡¯s equations in various situations, which is
essential if you are geared to applied physics and will pursue a related
research in the future. However, if you are geared to theoretical particle
physics, you may not need to know how to solve Maxwell¡¯s equations in all the various
situations, and may be more interested in the mathematical structure of electrodynamics
and Maxwell¡¯s equations. *No-Nonsense
Electrodynamics* does this job. *Introduction
to Electrodynamics *is more advanced than *Electricity and Magnetism*, but it is accessible to any college
student who has studied a little electromagnetism from freshman physics. At
Harvard, *Electricity and Magnetism* is
the textbook for the first course in electromagnetism for freshman physics
majors, showing that it does not require freshman physics as a prerequisite.
One thing to notice is that this book uses the CGS system, so the mathematical
formulas are a little different from those found in books using the MKS system.
However, the formulas are the same until one considers multiplicative factors,
and there is a table at the end of the Purcell¡¯s book comparing the formulas for
CGS and MKS. Multivariable calculus and mechanics are prerequisites to
electromagnetism. Many electromagnetism textbooks cover the basics of
multivariable calculus though.

**Waves**

ž *Waves: Berkeley Physics Course, Vol. 3* by Frank S. Crawford Jr.

ž *The Physics of Waves* by Georgi

__Comments__: I studied Crawford¡¯s book on my own and found it
easy to follow. It¡¯s too bad that this book seems to be out of print. *The Physics of Waves* should also be good
since it was written by a good teacher, but I have not read it. Understanding
waves is not hard, and all the material contained in the two books above is
treated in only one chapter of Goldstein¡¯s book on mechanics. Waves are not a
prerequisite to quantum mechanics, but an understanding of them allows one to
better appreciate quantum mechanics.

**Modern Physics**

ž *Concepts of Modern Physics* by Beiser

__Comments__: Some colleges offer a course called ¡®Modern
Physics,¡¯ but most of the material taught in such a course is also covered in a
quantum mechanics class. Therefore, modern physics is not a prerequisite to any
courses. I listed this book because its treatment of special relativity is
particularly good.

**Mathematical Methods for Physics**

ž *Mathematical Methods for Physics and Engineering* by Riley, Hobson, and
Bence

ž *Mathematical Methods for Physicists* by Arfken and Weber

ž *Mathematical Methods in the Physical Sciences* by Boas

ž *Schaum¡¯s Outline of Complex Variables* by Spiegel

__Comments__: Studying physics requires a solid
understanding of mathematics beyond freshman courses such as multivariable
calculus or linear algebra. It can be learned by taking either mathematics
courses designed for physics majors or by picking up in physics class- Most
physics students take such mathematics courses during their sophomore year.
However, instead of taking such courses, I ended up taking a complex analysis
course which was not designed for physics majors. *Schaum¡¯s Outline of
Complex Variables* was the textbook for my complex analysis course. It is cheap but clear. *Mathematical Methods for Physics and
Engineering* is the book I used for my independent studies and is my
favorite. The book by Arfken is the most popular book and is regarded as a
standard textbook, but it is not easy to follow for students who are learning
this material for the first time. I listed the book by Boas because it received
more stars than the book by Riley, Hobson and Bence and the book by Arfken on
Amazon.com.

**Quantum Mechanics**

ž *Quantum Mechanics Demystified *by McMahon

ž *No-Nonsense Quantum Mechanics: A Student-Friendly Introduction* by Schwichtenberg* *

ž *Principles of Quantum Mechanics* by Shankar

ž *Introduction to Quantum Mechanics* by Griffiths

ž *Modern Quantum Mechanics* by Sakurai

__Comments__: I first came across *Quantum Mechanics Demystified*, long after I learned quantum
mechanics and feel that it would be perfect for self-study by students with
minimal background. It gives a lot of explicit examples of calculations in
linear algebra which help you improve your understanding of quantum mechanics.
It would be suitable for students who have studied a little quantum mechanics
from my articles but want to learn more. Note that this book, like/unlike many
other books on quantum mechanics, introduces Schrödinger¡¯s equation before the
mathematical formalisms. This is possible because, loosely speaking,
Schrödinger¡¯s equation and the mathematical formalisms are not prerequisites to
one another. Readers can learn the mathematical formalisms of quantum mechanics
in chapters 4 through 8 more or less independently from the first three
chapters. Also, in the first reading, readers may skip the discussion on the
density operator. *No-Nonsense Quantum
Mechanics *is indeed student-friendly as the title suggests. The author
notes, ¡°Many textbooks are hard to understand, not because the subject is
difficult, but because the author can¡¯t remember what it¡¯s like to be a
beginner.¡± He notes that his book ¡°is written more like a casual conversation
with a more experienced student who shares with you everything he wished he had
known earlier.¡± While this book is not comprehensive, it gives a very
accessible explanation of some alternative interpretations to Copenhagen
interpretations, which no ordinary textbooks do. The other three books are all
favorites of mine and immensely helped me in understanding quantum mechanics. *Principles of Quantum Mechanics* is
suitable as either an undergraduate or graduate textbook, *Introduction to Quantum Mechanics* is suitable as an undergraduate
textbook, and *Modern Quantum Mechanics*
is suitable as a graduate textbook. Even though *Principles* can be used as a graduate textbook, it is easier to
follow than other books. It starts by covering the mathematical background
necessary for quantum mechanics and then goes on to review classical mechanics
to make a bridge between quantum mechanics and classical mechanics. *Introduction to Quantum Mechanics*, like
other books by

**Statistical Mechanics**

ž *Thermal Physics* by Kittel and Kroemer

ž *Fundamentals of Statistical and Thermal Physics* by Reif

__Comments__: I used *Thermal
Physics* when I first studied statistical mechanics. This book treats the
definition of temperature very well. While I myself have never read *Fundamentals of Statistical and Thermal
Physics*, it is regarded as a standard textbook in statistical mechanics. A
semester of quantum mechanics is helpful to understand statistical mechanics.

**Elementary Particle
Physics**

ž *Introduction to Elementary Particles* by David Griffiths

__Comments__: Many colleges offer an undergraduate course on
particle physics, even though one can learn all of the material from quantum
field theory courses which are at graduate level. However, it may be worth
glimpsing into what particle physics is all about without getting into all the
details or learning all the derivations of mathematical formulas. The book by

**General Relativity**

ž *Einstein Field
Equations –for beginners! *by DrPhysicsA (http://www.youtube.com/watch?v=foRPKAKZWx8)

ž *The Einstein Theory of Relativity: A Trip to the Fourth* Dimension by Lillian R.
Lieber

ž *A Most Incomprehensible
Thing: Notes Towards a Very Gentle Introduction to the Mathematics of
Relativity* by Peter Collier

ž *Introducing Einstein's Relativity* by d'Inverno

ž *A First Course in General Relativity* by Schutz

ž *Spacetime and Geometry: An Introduction to General Relativity* by Sean Carroll

__Comments__: Classical mechanics at the level of *Analytical Mechanics* by Cassiday and
Fowles is a formal prerequisite to Einstein¡¯s theory of general relativity, as
you need to understand what a Lagrangian is. However, the two-hour long video
by DrPhysicsA and the book by Lieber, which are both aimed at laymen,
successfully explains general relativity without this formal prerequisite. This
comes at the cost of leaving out the Lagrangian formulation of general
relativity, which is the most natural formulation. Therefore, a couple of
formulas must be taken for granted without thorough explanations, though Lieber
does indicate the relevant references. Nevertheless, as the only prerequisite
to this book is calculus, it seems that many young readers have benefitted from
it. This includes d¡¯Inverno, who noted in his book *Introducing Einstein¡¯s Relativity* that he was able to understand
general relativity at the age of 15 with the aid of Lieber¡¯s book. Lieber¡¯s
book also gives a very solid explanation of tensors, an indispensable
mathematical tool for general relativity. Albert Einstein himself called the
book ¡°A clear and vivid exposition of the essential ideas and methods of the
theory of relativity¡¦warmly recommended especially to those who cannot spend
too much time on the subject.¡± This book also covers special relativity. *A Most Incomprehensible Thing* is another
superb book on general relativity aimed at laymen. Compared to Lieber¡¯s book,
it is especially good, since it deals with calculus and classical mechanics at
a layman¡¯s level. Nevertheless, a couple of formulas must be taken for granted
as well. *Spacetime and Geometry* is
based on the author¡¯s lecture notes, available at (http://www.arxiv.org/abs/gr-qc/9712019).

**Quantum Effects in Gravity**

ž *Introduction to Quantum Effects in Gravity* by Mukhanov and Winitzki

ž *Quantum fields in curved space* by Birrell and Davies

__Comments__: Quantum effects in
gravity mainly concern things such as black hole entropy and Hawking radiation,
called ¡°black hole thermodynamics.¡± You have to know general relativity and
basic quantum field theory to understand these topics. However, basic quantum
field theory is covered in both of the above books. In particular, *Introduction to Quantum Effects in Gravity*
is well-written and easy to understand. The authors of this book recommend that
students study *Quantum fields in curved
space *or other advanced textbooks after reading their book.

**Hamiltonian Formulation of General Relativity and Loop Quantum Gravity**

ž *General Relativity* (Appendix E) by Robert M. Wald

ž *Quantum Gravity* by Carlo Rovelli

ž *Loop quantum gravity and quanta of space: a primer* by Carlo Rovelli and
Peush Upadhya (Lecture notes available at http://arxiv.org/abs/gr-qc/9806079)

ž *Lectures on Non-Perturbative Canonical Gravity* by Abhay Ashtekar

ž *Introductory lectures to loop quantum gravity* by Pietro Dona and Simone Speziale (Lecture notes
available at http://arxiv.org/abs/1007.0402))

ž *Covariant Loop Quantum Gravity* by Carlo Rovelli and Francesca Vidotto (Lecture
notes available at http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf

ž *Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance* by Marcus Gaul and Carlo Rovelli
(Lecture notes available at http://arxiv.org/abs/gr-qc/9910079)

ž *Loops, Knots,
Gauge Theories and Quantum Gravity *by* *Rodolfo Gambini and Jorge Pullin

ž *Background Independent Quantum Gravity: A Status* *Report* by Abhay Ashtekar and Jerzy Lewandowski (Lecture notes
available at http://arxiv.org/abs/gr-qc/0404018)

ž *Modern Canonical Quantum Gravity* by Thomas Thiemann (An earlier version available
at http://arxiv.org/abs/gr-qc/0110034)

ž *A Spin Network Primer* by Seth A. Major (Lecture notes available at http://arxiv.org/abs/gr-qc/9905020)

ž *A First Course in Loop Quantum Gravity*
by Rodolfo Gambini and Jorge Pullin

ž *Explorations in
Quantum Gravity* by Carlo Rovelli (14 video
lectures available at http://pirsa.org/C12012)

ž *Introduction to
Quantum Gravity* by Lee Smolin (25 video lectures
available at http://pirsa.org/C06001)

ž *The complete
spectrum of the area from recoupling theory in loop quantum gravity *(http://arxiv.org/abs/gr-qc/9608043)

ž *Geometry
Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity *(http://arxiv.org/abs/gr-qc/9602023)

__Comments__: The excellent treatment of the Hamiltonian
formulation of General Relativity in Appendix E of Wald¡¯s *General Relativity* helped me immensely, as I could not follow some
of the derivations in other references. The book by Rovelli and the lecture
notes by Rovelli and Upadhya were most helpful for me in understanding the
Ashtekar variable formulation of loop quantum gravity. The latter in particular
claimed to be ¡°self-contained¡± by the authors. Therefore, if you want to get a
basic idea of loop quantum gravity, you may want to read these lecture notes.
The book by Ashtekar, unfortunately, seems to be out of print. The book by
Thiemann is very mathematical and hard to follow after the first few chapters.
The lecture notes by Major discuss spin network, which is a central object in
loop quantum gravity. These lecture notes are easy to follow and accessible to
anyone with a solid knowledge of undergraduate quantum mechanics. Gambini and
Pullin¡¯s *A First Course in Loop Quantum Gravity* is targeted at
undergraduates and does not assume any knowledge of general relativity or of
quantum field theory. It devotes half of its pages to these two topics and
provides only a brief overview of loop quantum gravity without any deep
analysis or reasoning behind it. The video lectures by Rovelli and the others
by Smolin are good. The papers gr-qc/9608043 and gr-qc/9602023 show how the
area spectrum is calculated in loop quantum gravity. Even though the Ashtekar
variable formulation was discovered through the framework of the ADM Hamiltonian
formulation of general relativity as treated in Wald¡¯s book, the modern
treatment shows that the former no longer requires the latter as a
prerequisite; it is more beneficial from an educational standpoint to approach
Ashtekar variable formulation using vierbein and differential forms. Quantum
field theory is not a prerequisite to the Ashtekar variable formulation,
although Yang-Mills theory is. Nevertheless, a deeper understanding of loop
quantum gravity requires the knowledge of quantum field theory.

**Quantum Field Theory**

ž *A **First Book of Quantum Field Theory *by Lahiri and Pal

ž *Quantum **Field Theory in a Nutshell* by A. Zee

ž *Quantum Field
Theory and the Standard Model *by
Matthew D. Schwartz

ž *Quantum **Field Theory* by Lewis H. Ryder

ž *Quantum **Field Theory* by Mark Srednicki

ž *An **Introduction to Quantum Field Theory* by Peskin and Schroeder

ž *Conformal **Field Theory* (Chapter 2) by Philippe Di
Francesco, Pierre Mathieu, and David Senechal

ž *Aspects **of Symmetry* by Sidney Coleman

__Comments__: Quantum mechanics, special
relativity, and basic complex analysis (residue theorem) are prerequisites to
quantum field theory. The book by Peskin and Schroeder is regarded as a
standard textbook, even though it has a reputation of being more suitable for
students who intend to study phenomenology. The book by Lahiri and Pal seems to
be excellent, as the title would suggest, for students who are learning quantum
field theory for the first time. I regret that I didn¡¯t know of this book when
I first studied quantum field theory. This book treats concepts clearly and
concisely, and shows lucid derivations of formulas while providing essential
tools, unlike most books on quantum field theory, which sometimes spend too
many pages on somewhat inessential material which can be confusing for
beginners. On the other hand, this book doesn¡¯t treat important topics such as
the renormalization group, BRST symmetry, and anomalies which are essential but
could be somewhat difficult for beginners. Nevertheless, I recommend this book
to students who are anxious to learn quantum field theory as quickly as
possible. The book by Zee offers excellent
verbal explanations and is easy to follow. The book by Schwartz treats quantum field theory with a modern
perspective. I especially liked his ways of presenting subjects, which were
sometimes different from other textbooks. On the other hand, he also treats
quantum field theory à la Schwinger, which other modern textbooks no longer do.
In any case, I guess that Schwartz¡¯s book will soon replace the book by Peskin
and Schroeder as a standard textbook. The book by Ryder is easy to follow
and covers only the minimum necessary materials. The book by Srednicki is good
because it has many short chapters that explain concepts clearly. The book
¡®Conformal Field Theory¡¯ is not a quantum field theory textbook, but it
provides an overview of the very basics of the theory. I find this treatment
concise and clear. The book by Sidney Coleman is regarded as a classic. The
late Sidney Coleman was known to be a clear lecturer and was regarded as one of
the greatest leaders of quantum field theory. This book, which explores
materials other than what is covered in conventional quantum field theory
textbooks, explains important concepts such as instantons and 1/N expansion,
which are not usually covered in other quantum field theory textbooks. To
understand this book, you have to know some quantum field theory.

**Supersymmetry and Supergravity**

ž *Supersymmetry and Supergravity* by Julius Wess and Jonathan Bagger

ž *Introduction to Supersymmetry by Adel Bilal* (Lecture notes available at http://www.arxiv.org/abs/hep-th/0101055)

ž *Supersymmetric Gauge Field Theory and String* *Theory* by
David Bailin and Alexander Love

ž *An Introduction to Supergravity *by Cerdeno and Munoz (Lecture notes available at http://pos.sissa.it/archive/conferences/001/011/corfu98_011.pdf)

__Comments__: A year of quantum field
theory courses is a prerequisite to supersymmetry, while supersymmetry is a
prerequisite to supergravity. The book by Wess and Bagger is regarded as a
standard textbook for
supersymmetry, but I found the lecture
notes by Bilal easier to follow. As far as supersymmetry is concerned, the
material treated in these lecture notes is similar to that covered in the book
by Wess and Bagger, except for the fact that the lecture notes also cover the
non-linear sigma model and Seiberg-Witten duality. The book by Bailin and Love
is another book with which one can easily learn supersymmetry. As for
supergravity, I found the book by Bailin and Love and the lecture notes by
Cerdeno and Munoz concise. Most of the other books on supergravity spend many
pages deriving supergravity Lagrangian and transformation. If you are fine with
not knowing this complicated derivation, the book and the lecture notes I
mentioned should be fine. A string theorist told me that you don¡¯t usually need
to know this derivation.

**Lie Group Theory in Particle Physics**

ž *Lie Algebras in Particle Physics* by Howard Georgi

ž *Modern Quantum Mechanics* (Chapter 6.5) by Sakurai

ž *Quantum Field Theory in a Nutshell* (Appendix B) by A. Zee

ž *Conformal Field Theory* (Chapter 13) by Philippe Di Francesco, Pierre Mathieu, and David Senechal

__Comments__: *Lie
Algebras* seems adequate to understand isospin or the beautiful symmetries
relating many different particles, and how group theory is used in particle
physics. It is sometimes difficult to follow, and unfortunately, it is hard to
find an alternative that is any better. Still, I was able to understand the
basic concepts covered in this book well, after reading Chapter 6.5 of *Modern Quantum Mechanics* and Appendix B
of *Quantum Field Theory in a Nutshell*.
Without Georgi¡¯s book, however, these latter two alone are not enough to impart
a good understanding of group theory. Also, important concepts such as root and
weight can be learned more quickly by studying Chapter 13 of *Conformal Field Theory*. The treatment
there is simpler than that in Georgi¡¯s book and more to the point.

**String Theory**

ž *A First Course in String Theory* by Barton Zwiebach

ž *String Theory and M-Theory: A Modern Introduction* by Katrin Becker, Melanie Becker,
and John H. Schwarz

ž *String Theory, Vol. I, II* by Joseph Polchinski

ž *Joe¡¯s Little Book of String *by Joseph Polchinski: http://www.itp.ucsb.edu/~joep/JLBS.pdf

ž *Superstring Theory, Vol. 1, 2* by Michael B. Green, John H.
Schwarz, and Edward Witten

ž *Quantum Fields and Strings: A Course for Mathematicians
(Vol. 1 & 2) *

ž *Conformal Field Theory* (Chapter 4~6) by Philippe Di
Francesco, Pierre Mathieu, and David Senechal

ž *D-Branes* by Clifford V. Johnson

ž *Mirror Symmetry* by Kentaro Hori, Sheldon Katz,
Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil
and Eric Zaslow

ž *Lectures on Strings and Dualities* by Cumrun Vafa (http://arxiv.org/abs/hep-th/9702201)

ž *String Theory Wiki* (A website listing review papers
for many different specific areas of string theory): http://www.stringwiki.org/

__Comments__: *A First Course in String Theory *does not assume knowledge of
quantum field theory, so it is accessible to advanced undergraduates. All other
books on string theory assume knowledge of quantum field theory and general
relativity. *String Theory and M-Theory*
was praised by a string theorist Andrew Strominger as ¡°destined to become the
standard textbook.¡± As this book is new, it treats many new concepts such as
AdS/CFT correspondence and black hole entropy. *String Theory *by Polchinski was regarded as a standard textbook
before the book by Becker, Becker, and Schwarz was published. However,
Polchinski¡¯s book is not so easy to follow. Therefore, he wrote an easier book
titled ¡°Joe¡¯s Little Book of String.¡± The book by Green, Schwarz, and Witten is
rather old and omits many important recent developments, but it is still a good
book. *Quantum Fields and Strings* is
written for mathematicians, but many parts of this book are accessible to
physicists as well; many chapters were in fact written by physicists. For those
who already know much about the basics of quantum field theory, I highly
recommend the second volume of this book. The book *Conformal Field Theory* is not a string theory textbook but explains
the part of conformal field theory treated in the standard string theory
textbooks in a clearer and easier way. I personally found the treatment in this
book to be much more understandable than the explanation provided in the book
by Polchinski. The book by Johnson is a good book if you want to specialize in
D-branes which are central objects in string theory. The book *Mirror Symmetry* is a very good book if
you want to specialize in this subject. I have written more about this book in
the section ¡°Mirror Symmetry and Toric Geometry.¡± The lecture notes by Vafa are
intended for ¡°those with no previous background in string theory who wish to
join the research effort in this area,¡± but I found them useful even with a
background in string theory. Finally, as you study string theory, you will need
to read many review papers because much important material is not covered in
string theory textbooks. The website listed above can be helpful in such cases.

**Mathematics for String Theory**

ž *Geometry, Topology and Physics* by M. Nakahara

ž *Gravitation, Gauge Theories and Differential Geometry* by Eguchi, Gilkey, and Hanson
(Phys. Rept. 66 (1980) 213)

ž *Topology and Geometry for Physicists *by Charles Nash

ž *Geometrical Methods of Mathematical Physics *by Bernard F. Schutz

ž *Enumerative Geometry and String Theory* by Sheldon Katz

__Comments__: The book by Nakahara is intended
for students who study string theory. The Physics Report review paper is
concise and to the point, even though it covers some topics not covered in
Nakahara¡¯s book. I recommend that you study the Physics Report review paper
first, referencing Nakahara¡¯s book if and when you think you need more
explanation. The book by Nash handles math with
less rigor but tries to provide intuitive pictures. The book by Schutz is also
a very accessible book for physics students, but the material supplied is not
sufficient. The book by Katz is based on his
lectures at the summer school for undergraduates. As this book only assumes
knowledge of linear algebra and freshman physics, it is more accessible than
other books. Also, this book is clear and easy to understand; the author gives
a lot of motivations for specific definitions and theorems, and explains things
in a rather informal way. Not all branches of string theory, however, require
knowledge of enumerative geometry, and there are in any case many topics in
mathematics more essential than enumerative geometry.

**Conformal Field Theory**

ž *Conformal Field Theory* by Philippe Di Francesco, Pierre
Mathieu, and David Senechal

ž *Applied Conformal Field Theory by* Paul Ginsparg (http://arxiv.org/abs/hep-th/9108028)

__Comments__: String theory being conformal,
virtually all string theory textbooks deal with the basics of the conformal field
theory relevant thereto. However, it is well worth learning conformal field
theory in more detail, as it continues to play a critical role in deeper levels
of string theory. *Conformal Field Theory*
is a very thick book, which deals with this particular subject thoroughly yet
gently, showing the details of steps and calculations rather than leaving these
to the reader.

**AdS/CFT correspondence**

ž *Large N Field Theories, String Theory and Gravity* (http://arxiv.org/abs/hep-th/9905111)

ž *Introduction to AdS-CFT* by Horatiu Nastase (http://arxiv.org/abs/0712.0689)

ž *Supersymmetric Gauge Theories and the AdS/CFT Correspondence* by Eric D¡¯Hoker and Daniel Z.
Freedman (http://arxiv.org/abs/hep-th/0201253)

ž *TASI 2003 lectures on AdS/CFT *by Juan Maldacena (http://arxiv.org/abs/hep-th/0309246)

ž *Introduction to Gauge/Gravity Duality* by Joseph Polchinski (http://arxiv.org/abs/1010.6134)

__Comments__: The Maldacena conjecture suggesting
AdS/CFT correspondence was proposed in 1997 by Juan Maldacena, and the relevant
paper is the one most cited in string theory. Contemporary string theory
textbooks do deal with this subject, but it is helpful to read other review
articles as well. The first lecture notes are thorough, but some think that
they are a little bit out of date. The lecture notes by Nastase don¡¯t assume
familiarity with string theory. The other three sets of lecture notes are based
on lectures at TASI summer school.

**Topological Strings**

ž *A mini-course on topological strings* by Marcel Vonk (http://arxiv.org/abs/hep- th/0504147)

ž *Topological strings and their physical applications* by Andrew Neitzke and Cumrun
Vafa (http://arxiv.org/abs/hep-th/0410178)

__Comments__: Topological strings is an active
research area of string theory. Assuming only the general knowledge of string
theory, the lecture notes by Vonk seem to be the most accessible introduction
to this subject. Vonk also recommends the readers to read the lecture notes by
Neitzke and Vafa after finishing his own lecture notes.

**Mirror Symmetry and Toric Geometry**

ž *Mirror Symmetry* by Kentaro Hori, Sheldon Katz,
Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil
and Eric Zaslow

ž *Les Houches Lectures on Constructing String Vacua *(Section 5)* *by Frederik Denef (https://arxiv.org/pdf/0803.1194.pdf)

ž *String Theory on Calabi-Yau Manifolds* by Brian R. Greene (http://arxiv.org/abs/hep-th/9702155)

ž *Lectures on Mirror Symmetry* by S. Hosono, A. Klemm and S.
Theisen (http://arxiv.org/abs/hep-th/9403096)

ž *Toric geometry and local Calabi-Yau varieties – An introduction
to toric geometry (for physicists)* by Cyril Closset (http://arxiv.org/abs/0901.3695)

ž *Lectures on complex geometry, Calabi-Yau manifolds and toric
geometry*
by Vincent Bouchard (http://arxiv.org/abs/hep-th/0702063)

ž *String Dualies and Toric Geometry: An Introduction* by Harald Skarke (http://arxiv.org/abs/hep-th/9806059)

ž *Introduction to Toric Varieties* by William Fulton

__Comments__: Mirror symmetry and toric geometry
are active research areas in string theory and mathematics. The book *Mirror Symmetry* is a very thick book
which deals with these subjects. This book offers both mathematical and
physical points of views of this subject. Remarkably, this book teaches all the
physics prerequisites required to understand mirror symmetry, such as quantum
mechanics or quantum field theory, for mathematicians who know nothing about
physics. However, a solid background in physics will make the subject much
easier to understand. I included the *Les
Houches Lecture* notes by Frederik Denef here because after reading them, I
was able to understand some of the parts that I could not understand in the
book *Mirror Symmetry*. *String Theory on Calabi-Yau Manifolds* is
written by the author of the popular book ¡°The Elegant Universe.¡± These lecture
notes and *Lectures on Mirror Symmetry*
are helpful to understand mirror symmetry. The lecture notes by Closset nicely
and briefly introduce ¡°the gist¡± of the algebraic geometry on which to build
toric geometry. The book by Fulton is not targeted at physicists but at
mathematicians.