Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics

Book Details:

• Publisher: Dover

• Author: Palle E.T. Jorgensen

• Language: English

• Edition: 3rd ed.

• ISBN: 0800759815722

• Pages: 304

• Binding: Paperback

• Release Date: 21-06-2017

• Dimensions: 9.2 x 6.2 x 0.6 inches

About The Book:

Operators and Representation Theory by Palle E.T. Jorgensen is a comprehensive monograph suitable for advanced undergraduates and graduate students in mathematics and physics. The book is divided into three distinct parts, each providing an in-depth exploration of operators and representation theory, with a focus on the intersection of mathematics and physics.

The first part introduces essential background material on definitions, terminology, and operators in Hilbert space. It concludes with a discussion on the imprimitivity theorem, providing a more mathematical approach to Wigner’s work on representations of the Poincaré and Galilei groups. This foundational section ensures readers have a solid understanding of key concepts before moving into more complex discussions.

The second part delves into the algebras of operators in Hilbert space, expanding on the mathematics used in earlier quantum theory versions. It explores how the Hamiltonian operator, which governs the time translation of quantum systems, can be represented as a polynomial in elements of an underlying Lie algebra. This section also addresses the properties of such operators, offering numerous examples for clarity.

The final part of the book focuses on covariant representations and connections, with a particular emphasis on infinite-dimensional Lie algebras. The text highlights the importance of mathematical physics throughout, emphasizing the real-world applications of these theories. To enhance understanding, the book concludes with three valuable appendices, including a comprehensive Guide to the Literature.

This book is an essential resource for students and professionals eager to understand the advanced mathematical structures that underpin quantum theory and its applications in physics.