Quantum Spin and Representations of the Poincaré Group, Part I: With a Focus on Physics and Operator Theory (Synthesis Lectures on Engineering, Science, and Technology)

Synopsis

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 I of Quantum Spin and Representations of the Poincaré Group specifically addresses: conventions; basic properties of SO(2) and SO(3); construction of a double cover of SO(3); SU(2) spinors; continuous unitary representation of SU(2); basic properties of the Lorentz Group; unitary representation of the restricted Lorentz Group; an extension to a strongly continuous representation of the restricted Poincaré Group; and an extension to a unitary/anti-unitary representation of the Poincaré Group.

Copyright:

2026

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9783031841408

Related ISBNs:

9783031841392

Publisher:

Springer Nature Switzerland

Date of Addition:

06/02/25

Copyrighted By:

The Editor

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Science, Earth Sciences, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.