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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.
List of 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.
About the author
Horst R. Beyer, Ph.D., is currently affiliated with the University of Tuebingen Institute for Astronomy and Astrophysics, Theoretical Astrophysics Division. Dr. Beyer has written 8 books and 39 published articles. His research interests include mathematical physics, in particular the applications of operator theory in quantum field theory, general relativity, astrophysics, and the engineering sciences.
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 specificallyaddresses: 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.
