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BL
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| Record Number
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972880
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b727250
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| Main Entry
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Kaiser, G.
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| Title & Author
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Quantum Physics, Relativity, and Complex Spacetime : towards a new synthesis.
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| Publication Statement
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Burlington :: Elsevier Science,, 1990.
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| Series Statement
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North-Holland mathematics studies ;; v.163
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| Page. NO
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1 online resource (377 p.).
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| ISBN
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0080872743
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: 1281782939
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: 6611782931
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: 9780080872742
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: 9781281782939
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: 9786611782931
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| Notes
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Description based upon print version of record.
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| Contents
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Front Cover; Quantum Physics, Relativity, and Complex Spacetime: Towards a New Synthesis; Copyright Page; Contents; Preface; Suggestions to the Reader; Chapter 1. Coherent-State Representations; 1.1. Preliminaries; 1.2. Canonical Coherent States; 1.3. Generalized Frames and Resolutions of Unity; 1.4. Reproducing-Kernel Hilbert Spaces; 1.5. Windowed Fourier Transforms; 1.6. Wavelet Transforms; Chapter 2. Wavelet Algebras and Complex Structures; 2.1. Introduction; 2.2. Operational Calculus; 2.3. Complex Structure; 2.4. Complex Decomposition and Reconstruction; 2.5. Appendix
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5.4. Free Klein-Gordon Fields5.5. Free Dirac Fields; 5.6. Interpolating Particle Coherent States; 5.7. Field Coherent States and Functional Integrals; Notes; Chapter 6. Further Developments; 6.1. Holomorphic Gauge Theory; 6.2. Windowed X-Ray Transforms: Wavelets Revisited; References; Index
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Chapter 3. Frames and Lie Groups3.1. Introduction; 3.2. Klauder's Group-Frames; 3.3. Perelomov's Homogeneous G-Frames; 3.4. Onofri's Holomorphic G-Frames; 3.5. The Rotation Group; 3.6. The Harmonic Oscillator as a Contraction Limit; Chapter 4. Complex Spacetime; 4.1. Introduction; 4.2. Relativity, Phase Space and Quantization; 4.3. Galilean Frames; 4.4. Relativistic Frames; 4.5. Geometry and Probability; 4.6. The Non-Relativistic Limit; Notes; Chapter 5. Quantized Fields; 5.1. Introduction; 5.2. The Multivariate Analytic-Signal Transform; 5.3. Axiomatic Field Theory and Particle Phase Spaces
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| Abstract
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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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Mathematical physics.
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Quantum theory.
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Relativity (Physics)
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Space and time.
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Mathematical physics.
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Quantum theory.
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Relativity (Physics).
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Space and time.
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Atomic Physics.
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Mathematical physics.
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Physical Sciences Mathematics.
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Physics.
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Quantum theory.
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Relativity (Physics)
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Space and time.
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| Dewey Classification
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530.1/2 20530.12
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| LC Classification
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QC174.12 .K34 1990
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QC174.12.K
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| Parallel Title
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North-Holland Mathematics Studies Vol. 163
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