Quantum Theory Basics

Abstract

Quantum Theory Basics gives a modern review of quantum theory, including quantum mechanics and (mostly path-integral based) quantum field theory, as well as Abelian and non-Abelian gauge theories with their quantization. It includes the following sections:

• 3.1 Basics of Non-Relativistic Quantum Mechanics

  This section introduces Schrödinger-Dirac quantum mechanics of a single particle and system of particles.

• 3.2 Introduction to Quantum Fields

  This section includes Dirac’s amplitude, causality and QED, free and interacting quantum fields, Abelian gauge fields and introduction to topological quantum computation.

• 3.3 The Feynman Path Integral

  This section introduces Feynman’s action-amplitude formalism, correlation functions and generating functionals, Feynman QED, and wavelet-based QFT.

• 3.4 The Path-Integral TQFT

  This section briefly describes Schwarz- and Witten-type quantum field theories, presents topological Hodge decomposition theorem and its application to Chern-Simons theory.

• 3.5 Non-Abelian Gauge Theories

  This section introduces Yang-Mills theory and its quantization.