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

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 is the relativistic generalization of Schrödinger equation.

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.

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 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

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 articles here are very beautiful and elegant.

The Dirac field

C, P, T transformation for the Dirac field

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

Connected diagrams and disconnected diagrams

The effective action

Wick rotation

Euclidean formulation

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

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

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

Tensor methods

Clebsch-Gordan decomposition

Quark model

SU(5) and the Georgi-Glashow model