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Quantum Physics, Relativity, and Complex Spacetime - 1st Edition - ISBN: 9780444884657, 9780080872742

Quantum Physics, Relativity, and Complex Spacetime, Volume 163

1st Edition

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Author: G. Kaiser
eBook ISBN: 9780080872742
Imprint: North Holland
Published Date: 11th December 1990
Page Count: 358
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Table of Contents

1. Coherent-State Representations. Preliminaries. Canonical Coherent States. Generalized Frames and Resolutions of Unity. Reproducing-Kernel Hilbert Spaces. Windowed Fourier Transforms. Wavelet Transforms. 2. Wavelet Algebras and Complex Structures. Introduction. Operational Calculus. Complex Structure. Complex Decomposition and Reconstruction. Appendix. 3. Frames and Lie Groups. Introduction. Klauder's Group-Frames. Perelomov's Homogeneous G-Frames. Onofri's Holomorphic G-Frames. The Rotation Group. The Harmonic Oscillator as a Contraction Limit. 4. Complex Spacetime. Introduction. Relativity, Phase Space and Quantization. Galilean Frames. Relativistic Frames. Geometry and Probability. The Non-Relativistic Limit. Notes. 5. Quantized Fields. Introduction. The Multivariate Analytic-Signal Transform. Axiomatic Field Theory and Particle Phase Spaces. Free Klein-Gordon Fields. Free Dirac Fields. Interpolating Particle Coherent States. Field Coherent States and Functional Integrals. Notes. 6. Further Developments. Holomorphic Gauge Theory. Windowed X-Ray Transforms: Wavelets Revisited. References. Index.


A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.


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© North Holland 1990
11th December 1990
North Holland
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@qu:A lucid text filled with carefully developed mathematics. @source:The American Mathematical Monthly

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About the Author

G. Kaiser

Affiliations and Expertise

Department of Mathematics, University of Lowell, Lowell, MA, USA