The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by Brian Greene
The Theoretical Minimum: What You Need to Know to Start Doing Physics by Leonard Susskind and George Hrabovsky
The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose
A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity by Peter Collier
The Character of Physical Law by Richard Feynman
QED: The Strange Theory of Light and Matter by Richard Feynman
Feynman¡¯s Lost Lecture: The Motion of Planets around the Sun
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
Surely, You¡¯re Joking Mr. Feynman! (Adventures of a Curious Character) by Richard Feynman.
A Passion for Discovery by Peter Freund
The Recollections of
Physics and Beyond, Encounters and Conversations by Werner Heisenberg
Schrödinger: 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. Schrödinger: 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
Who is Fourier? A Mathematical Adventure by Transnational College of LEX
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)
Subtle is the Lord: The Science and the Life of Albert Einstein by Abraham Pais
Inward Bound: Of Matter and Forces in the Physical World by Abraham Pais .
The Historical Development of Quantum Theory, Vol 1~6 by Jagdish Mehra and Helmet Rechenberg
QED and the Men Who Made
It by Silvan
Einstein¡¯s Unification by Jeroen van Dongen
The Supersymmetric World: The Beginnings of the Theory by Gordon L. Kane and Mihail A. Shifman
The Birth of String Theory by Dr. Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia
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. 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.
What is Mathematics? An Elementary Approach to Ideas and Methods by Courant, Robbins, and Stewart
Calculus and Analytic Geometry by Thomas and Finney
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.
Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach by Hubbard
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)
Fundamentals of Physics by Halliday, Resnick, and Walker
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.
Analytical Mechanics by Cassiday and Fowles
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.
Electricity and Magnetism (Berkeley Physics Course) by Purcell
Introduction to Electrodynamics by Griffiths
Comments: Both of these two books are very well-written and easy to follow. 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.
Waves: Berkeley Physics Course, Vol. 3 by Frank S. Crawford Jr.
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.
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 can be 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
Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence
Mathematical Methods for Physicists by Arfken and Weber
Mathematical Methods in the Physical Sciences by Boas
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 Demystified by McMahon
Principles of Quantum Mechanics by Shankar
Introduction to Quantum Mechanics by Griffiths
Modern Quantum Mechanics by Sakurai
Comments: I recently came across Quantum Mechanics Demystified, 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.
Therefore, it differs from my approach in which mathematical formalisms are
introduced first. 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. 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
Thermal Physics by Kittel and Kroemer
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
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
Einstein Field Equations –for beginners! by DrPhysicsA (http://www.youtube.com/watch?v=foRPKAKZWx8)
The Einstein Theory of Relativity: A Trip to the Fourth Dimension by Lillian R. Lieber
A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity by Peter Collier
Introducing Einstein's Relativity by d'Inverno
A First Course in General Relativity by Schutz
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
Introduction to Quantum Effects in Gravity by Mukhanov and Winitzki
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
General Relativity (Appendix E) by Robert M. Wald
Quantum Gravity by Carlo Rovelli
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)
Lectures on Non-Perturbative Canonical Gravity by Abhay Ashtekar
Introductory lectures to loop quantum gravity by Pietro Dona and Simone Speziale (Lecture notes available at http://arxiv.org/abs/1007.0402))
Covariant Loop Quantum Gravity by Carlo Rovelli and Francesca Vidotto (Lecture notes available at http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf
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)
Loops, Knots, Gauge Theories and Quantum Gravity by Rodolfo Gambini and Jorge Pullin
Background Independent Quantum Gravity: A Status Report by Abhay Ashtekar and Jerzy Lewandowski (Lecture notes available at http://arxiv.org/abs/gr-qc/0404018)
Modern Canonical Quantum Gravity by Thomas Thiemann (An earlier version available at http://arxiv.org/abs/gr-qc/0110034)
A Spin Network Primer by Seth A. Major (Lecture notes available at http://arxiv.org/abs/gr-qc/9905020)
A First Course in Loop Quantum Gravity by Rodolfo Gambini and Jorge Pullin
Explorations in Quantum Gravity by Carlo Rovelli (14 video lectures available at http://pirsa.org/C12012)
Introduction to Quantum Gravity by Lee Smolin (25 video lectures available at http://pirsa.org/C06001)
The complete spectrum of the area from recoupling theory in loop quantum gravity (http://arxiv.org/abs/gr-qc/9608043)
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
A First Book of Quantum Field Theory by Lahiri and Pal
Quantum Field Theory in a Nutshell by A. Zee
Quantum Field Theory and the Standard Model by Matthew D. Schwartz
Quantum Field Theory by Lewis H. Ryder
Quantum Field Theory by Mark Srednicki
An Introduction to Quantum Field Theory by Peskin and Schroeder
Conformal Field Theory (Chapter 2) by Philippe Di Francesco, Pierre Mathieu, and David Senechal
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
Supersymmetry and Supergravity by Julius Wess and Jonathan Bagger
Introduction to Supersymmetry by Adel Bilal (Lecture notes available at http://www.arxiv.org/abs/hep-th/0101055)
Supersymmetric Gauge Field Theory and String Theory by David Bailin and Alexander Love
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
Lie Algebras in Particle Physics by Howard Georgi
Modern Quantum Mechanics (Chapter 6.5) by Sakurai
Quantum Field Theory in a Nutshell (Appendix B) by A. Zee
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.
A First Course in String Theory by Barton Zwiebach
String Theory and M-Theory: A Modern Introduction by Katrin Becker, Melanie Becker, and John H. Schwarz
String Theory, Vol. I, II by Joseph Polchinski
Joe¡¯s Little Book of String by Joseph Polchinski: http://www.itp.ucsb.edu/~joep/JLBS.pdf
Superstring Theory, Vol. 1, 2 by Michael B. Green, John H. Schwarz, and Edward Witten
Quantum Fields and Strings: A Course for Mathematicians (Vol. 1 & 2)
Conformal Field Theory (Chapter 4~6) by Philippe Di Francesco, Pierre Mathieu, and David Senechal
D-Branes by Clifford V. Johnson
Mirror Symmetry by Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil and Eric Zaslow
Lectures on Strings and Dualities by Cumrun Vafa (http://arxiv.org/abs/hep-th/9702201)
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
Geometry, Topology and Physics by M. Nakahara
Gravitation, Gauge Theories and Differential Geometry by Eguchi, Gilkey, and Hanson (Phys. Rept. 66 (1980) 213)
Topology and Geometry for Physicists by Charles Nash
Geometrical Methods of Mathematical Physics by Bernard F. Schutz
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
Conformal Field Theory by Philippe Di Francesco, Pierre Mathieu, and David Senechal
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.
Large N Field Theories, String Theory and Gravity (http://arxiv.org/abs/hep-th/9905111)
Introduction to AdS-CFT by Horatiu Nastase (http://arxiv.org/abs/0712.0689)
Supersymmetric Gauge Theories and the AdS/CFT Correspondence by Eric D¡¯Hoker and Daniel Z. Freedman (http://arxiv.org/abs/hep-th/0201253)
TASI 2003 lectures on AdS/CFT by Juan Maldacena (http://arxiv.org/abs/hep-th/0309246)
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.
A mini-course on topological strings by Marcel Vonk (http://arxiv.org/abs/hep-th/0504147)
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
Mirror Symmetry by Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil and Eric Zaslow
Les Houches Lectures on Constructing String Vacua (Section 5) by Frederik Denef (https://arxiv.org/pdf/0803.1194.pdf)
String Theory on Calabi-Yau Manifolds by Brian R. Greene (http://arxiv.org/abs/hep-th/9702155)
Lectures on Mirror Symmetry by S. Hosono, A. Klemm and S. Theisen (http://arxiv.org/abs/hep-th/9403096)
Toric geometry and local Calabi-Yau varieties – An introduction to toric geometry (for physicists) by Cyril Closset (http://arxiv.org/abs/0901.3695)
Lectures on complex geometry, Calabi-Yau manifolds and toric geometry by Vincent Bouchard (http://arxiv.org/abs/hep-th/0702063)
String Dualies and Toric Geometry: An Introduction by Harald Skarke (http://arxiv.org/abs/hep-th/9806059)
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.