Quantum Spin and Representations of the Poincaré Group, Part II : With a Focus on Physics and Operator Theory / by Horst R. Beyer.

Format:

Book

Author/Creator:

Beyer, Horst R.

Series:

Synthesis Lectures on Engineering, Science, and Technology, 2690-0327

Language:

English

Subjects (All):

Particles (Nuclear physics).

Quantum field theory.

Mathematical physics.

Quantum theory.

Operator theory.

Physics.

Astronomy.

Elementary Particles, Quantum Field Theory.

Theoretical, Mathematical and Computational Physics.

Quantum Physics.

Operator Theory.

Mathematical Physics.

Physics and Astronomy.

Local Subjects:

Elementary Particles, Quantum Field Theory.

Theoretical, Mathematical and Computational Physics.

Quantum Physics.

Operator Theory.

Mathematical Physics.

Physics and Astronomy.

Physical Description:

1 online resource (218 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This book discusses how relativistic quantum field theories must transform under strongly continuous unitary representations of the Poincaré group. The focus is on the construction of the representations that provide the basis for the formulation of current relativistic quantum field theories of scalar fields, the Dirac field, and the electromagnetic field. Such construction is tied to the use of the methods of operator theory that also provide the basis for the formulation of quantum mechanics, up to the interpretation of the measurement process. In addition, since representation spaces of primary interest in quantum theory are infinite dimensional, the use of these methods is essential. Consequently, the book also calculates the generators of relevant strongly continuous one-parameter groups that are associated with the representations and, where appropriate, the corresponding spectrum. Part II of Quantum Spin and Representations of the Poincaré Group specifically addresses: construction of a double cover of the restricted Lorentz Group; Weyl spinors; Weyl representation of SL(2, C); an extension to a strongly continuous representation of a semi-direct product of R^4 and SL(2, C); Dirac spinors; Dirac fields; Dirac equation; Spin 1 representations of SL(2, C); Maxwell fields; and Maxwell's equations. In addition, this book: Presents how the use of methods from operator theory have become an indispensable tool for quantum field theory Connects mathematical results with their applications in physics, particularly in quantum field theory Provides mathematical rigor, introduces physical constants, and presents the dimensions of physical quantities.

Contents:

Introduction

Construction of a Double Cover of the Restricted Lorentz Group

Weyl Spinors

Weyl Representation of SL(2, C)

An Extension to a Strongly Continuous Representation of a Semi-direct Product of R^4 and SL(2, C)

Dirac Spinors

Dirac Fields

Dirac Equation

Spin 1 Representations of SL(2, C)

Maxwell Fields

Maxwell's Equations

Appendix

Bibliography

Index of Symbols

Index.

ISBN:

3-031-95823-3