Mathematics of Quantization and Quantum Fields

This book provides a comprehensive review of mathematical aspects of quantization and quantum field theory, covering canonical commutation and anti-commutation relations, free bosonic and fermionic fields, and interacting fields. It is essential reading for graduate students and researchers in mathematics and physics.

Format: Paperback / softback
Length: 688 pages
Publication date: 09 February 2023
Publisher: Cambridge University Press

Quantum field theory is a fundamental branch of physics that describes the behavior of matter and energy at the atomic and subatomic levels. It is a complex and mathematical theory that requires a deep understanding of mathematics, including quantum mechanics, linear algebra, and differential equations. In this book, we will explore the mathematical aspects of quantum field theory, including the theory of quantum mechanics, the quantization of fields, and the construction of field theories.

The theory of quantum mechanics is the foundation of quantum field theory. It describes the behavior of particles and their interactions with each other and with the electromagnetic field. Quantum mechanics is based on the principles of wave-particle duality, which states that particles can be described as both waves and particles at the same time. This duality is a result of the fact that particles have both a wave-like and a particle-like nature.

Quantization of fields is a key concept in quantum field theory. It is the process of assigning a discrete set of values to the energy and momentum of particles in a field. The energy and momentum of particles in a field are quantized in units of energy and momentum, respectively. The quantization of fields is a result of the fact that the energy and momentum of particles in a field are limited by the Planck constant, which is a fundamental constant of nature.

The construction of field theories is a key aspect of quantum field theory. Field theories are mathematical models that describe the behavior of particles and fields at the atomic and subatomic levels. They are used to describe a wide range of physical phenomena, including the behavior of matter, the behavior of light, and the behavior of the universe. There are two main types of field theories: gauge field theories and particle field theories.

Gauge field theories are used to describe the behavior of particles that interact with each other through the electromagnetic field. They are based on the principle
Principles of gauge symmetry, which states that the laws of physics are invariant under certain transformations that preserve the gauge symmetry of the theory. Gauge field theories are used to describe a wide range of physical phenomena, including the behavior of elementary particles, the behavior of matter, and the behavior of the universe.

Particle field theories are used to describe the behavior of particles that interact with each other through the strong nuclear force. They are based on the principles of particle physics, which states that the laws of physics are invariant under certain transformations that preserve the particle number of particles. Particle field theories are used to describe a wide range of physical phenomena, including the behavior of elementary particles, the behavior of matter, and the behavior of the universe.

In conclusion, quantum field theory is a complex and mathematical theory that requires a deep understanding of mathematics, including quantum mechanics, linear algebra, and differential equations. This book field theory is a fundamental branch of physics that describes the behavior of matter and energy at the atomic and subatomic levels. It is a complex and mathematical theory that requires a deep understanding of mathematics, including quantum mechanics, linear algebra, and differential equations. In this book, we will explore the mathematical aspects of quantum field theory, including the theory of quantum mechanics, the quantization of fields, and the construction of field theories.

ISBN-13: 9781009290838