Quantum physics, relativity, and complex spacetime : towards a new synthesis
著者
書誌事項
Quantum physics, relativity, and complex spacetime : towards a new synthesis
（North-Holland mathematics studies, 163）
North-Holland , Distributors for the U.S.A. and Canada, Elsevier Science, 1990
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注記
Bibliographical references: p. 347-356
Includes index
内容説明・目次
内容説明
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.
目次
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.
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