**Introduction**

Quantum field theory is the
relativistic generalization of (non-relativistic) quantum mechanics. It is a
very huge subject which physics graduate students normally study for two or
three semesters after finishing graduate-level quantum mechanics in their first
year of study. Nevertheless, as ¡°Fundamental Physics Prize¡± laureate Prof. Nima
Arkani-Hamed did in his third year as a physics undergraduate, many students
successfully learn quantum field theory without the knowledge of graduate level
quantum mechanics; along with the very basics of special relativity and
Cauchy¡¯s residue theorem, undergraduate quantum mechanics is more or less
sufficient as a prerequisite.

In these articles, we will teach you
quantum field theory assuming you have already read my previous articles on
physics and math. Since I treated there several topics usually treated in
quantum field theory textbook, you may not understand some of our articles here
if you only know the very basics of special relativity and undergraduate
quantum mechanics without reading my previous articles on physics and math.

I will add more sections and
articles later.

**Preliminaries**

Notations and conventions
in our review articles for quantum field theory

__Comments:__

Every quantum field theory book uses
slightly different notations and conventions. In the first article, we will set
ours.

**Klein-Gordon equation and Noether¡¯s
theorem**

Klein-Gordon
equation and Klein-Gordon action

__Comments:__

Klein-Gordon equation is the
relativistic generalization of Schrödinger equation.

Noether¡¯s
theorem in field theory

__Comments__:

The first article explains the field theory
version of Noether¡¯s theorem which is the one familiar from classical
mechanics. Only minor details are different. The second article treats one of
the most important examples of Noether¡¯s theorem.

A simple derivation of the conserved current in
complex Klein-Gordon theory

The variation of a field in terms of the
Noether charge

__Comments__:

If an action exhibits a
symmetry, one can easily derive the conserved current using Noether¡¯s theorem.
However, there is an equivalent, easier method, if you cannot readily remember
the formula for Noether¡¯s theorem. The first article concerns this method. The
second article shows how the variation of a field can be expressed by the
Noether charge associated with the variation. Readers should be familiar with
this from my earlier article ¡°Noether¡¯s theorem in field theory.¡± However, I
approach this from a different perspective. These two articles concern concepts
which are very important and often used in quantum field theory, but which are
usually left out of textbooks.

**Complex
analysis**

Cauchy¡¯s
integral formula and Cauchy¡¯s residue theorem

Application
of residue theorem

__Comments:__

Cauchy¡¯s residue theorem plays an important role in quantum
field theory. For our purpose, it is needed in our article ¡°The Feynman
propagator¡± in the section ¡°Quantization of the scalar field.¡±

**Quantization
of the scalar field**

The
scalar field as harmonic oscillators

The
Feynman propagator of the scalar field

__Comments:__

By building on the ideas in the section ¡°Klein-Gordon
equation and Noether¡¯s theorem¡± we quantize Klein-Gordon field (also known as
the scalar field) in this section.

**The Lorentz
group**

The
Lorentz group and its representations

Spinor
representations of the Lorentz group

__Comments:__

The articles here are very beautiful and elegant.

**The Dirac
field**

The Dirac
equation and gamma matrices

Angular momentum
of the Dirac field

Solutions
of the Dirac equation

Quantization
of the Dirac field

The
Feynman propagator of the Dirac field

Electron
magnetic moment from the Dirac equation

C, P, T transformation for the Dirac field

__Comments:__

Having dealt with the scalar field in earlier sections, we
deal with the next simplest field, namely, the Dirac field in this section. In
the first reading, you can skip the last article.

**Scattering**

Cross sections

**Perturbation
theory**

The Dyson series
and the perturbative expansion of n-point function

Expectation
values in quantum field theory, revisited

Feynman
rules for phi^4 theory I

Feynman
rules for phi^4 theory II

Tree diagrams
and loop diagrams

Connected diagrams and disconnected diagrams

The effective action

Wick rotation

Euclidean formulation

__Comments:__

Those of the readers who read my earlier article
¡°Expectation values in quantum field theory (1)¡± may wonder why the Gaussian
function is present in the definition of the formula for the expectation
values. You will find the reason in the article about the Expectation values.

**Quantum
Electrodynamics**

Quantization of electromagnetic field

__Comments:__

You have to know the Maxwell
Lagrangian to understand the article ¡°Quantization of electromagnetic field¡±

**Renormalization**

**Path
Integral for Fermions**

**Quantization
of Non-Abelian Gauge theory**

Faddeev-Popov Ghost

BRST symmetry

Feynman rules for non-Abelian gauge theory

Asymptotic freedom

**Standard
Model**

Spontaneous symmetry breaking

Higgs mechanism

Glashow-Weinberg-Salam model

GIM mechanism and CKM matrix

**Anomalies**

**Group Theory**

SU(3) and the
Gell-Mann matrices

Tensor methods

Clebsch-Gordan decomposition

Quark model

SU(5) and the Georgi-Glashow model