Group Representation for Quantum Theory

Book Details

• Author: Masahito Hayashi

• Publisher: Springer

• Edition: 1st ed. 2017

• Binding: Hardcover

• Pages: 338

• Release Date: 28-11-2016

• ISBN: 9783319449043

• Dimensions: 9.4 x 6.3 x 1.0 inches

• Languages: English

About the Book

Group Representation Theory for Quantum Theory by Masahito Hayashi is a comprehensive text that addresses the application of group representation theory in quantum theory. The book is designed to bridge the gap between the highly abstract mathematical formulations of group theory and their practical applications in quantum physics.

The book covers a broad range of topics, including:

• Permutation Groups

• SU(2) and SU(d) Groups

• Heisenberg Representation

• Squeezing Operation

• Discrete Heisenberg Representation

• Relation with Fourier Transform

These topics are critical for understanding quantum systems, particularly in fields like angular momentum, hydrogen-type Hamiltonians, spin-orbit interactions, and quantum optics.

Key Features:

• Unified Approach: Hayashi takes a unified approach by exploring different aspects of representation theory from a quantum perspective. This includes projective representations, which are particularly significant in quantum theory.

• Target Audience: The book is aimed at both mathematicians and physicists, offering a clear and detailed explanation for those working with quantum theory. It fills the gap between mathematical rigor and physical applications.

• Clear Progression: The text starts with basic mathematical concepts before progressing to more complex topics like Lie groups and Lie algebras, making the material accessible for advanced students and researchers in physics and mathematics.

• Application Focus: Practical applications of the theory are discussed in detail, particularly in areas of quantum theory such as quantum information processing, quantum error correction, and the quark model.

Who Should Read This Book:

• Graduate Students: Ideal for graduate students in quantum mechanics, quantum field theory, or mathematical physics.

• Researchers and Physicists: Particularly those working on advanced quantum theory, group theory, and related fields such as quantum optics and information theory.

• Mathematicians: The book is also beneficial for those with a mathematical background interested in the application of group representation theory to quantum systems.

This book is an excellent resource for understanding how the abstract mathematical language of group theory can be applied to the concrete problems of quantum mechanics and quantum information theory.