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Quantum Spin and Representations of the Poincare Group, Part I : With a Focus on Physics and Operator Theory - Horst R. Beyer

Quantum Spin and Representations of the Poincare Group, Part I

With a Focus on Physics and Operator Theory

By: Horst R. Beyer

eText | 2 June 2025

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This book discusses how relativistic quantum field theories must transform under strongly continuous unitary representations of the Poincare 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 Poincare Group specificallyaddresses: 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 Poincare Group; and an extension to a unitary/anti-unitary representation of the Poincare Group.

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Non-FictionSciencePhysicsParticle & High-Energy PhysicsMathematical PhysicsQuantum Physics & Quantum Mechanics & Quantum Field TheoryMathematicsCalculus & Mathematical AnalysisFunctional Analysis & Transforms

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