Quantization methods: A guide for physicists and analysts

Ali  ST; Englis  M

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Quantization methods: A guide for physicists and analysts

机译：Quantization methods: A guide for physicists and analysts

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This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin-Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationships between various methods, their relative successes and shortcomings, mentioning also open problems in the area. Finally, even for approaches for which lack of space or expertise prevented us from treating them to the extent they would deserve, we have tried to provide ample references to the existing literature on the subject. In all cases, we have made an effort to keep the discussion accessible both to physicists and to mathematicians, including non-specialists in the field.

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《Reviews in mathematical physics》 |2005年第4期|391-490|共100页
作者
Ali ST; Englis M;
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作者单位

Concordia Univ, Dept Math & Stat, Montreal, PQ H4B 1R6, Canada;

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正文语种英语
中图分类理论物理学;
关键词
canonical quantization; borel quantization; geometric quantization; deformation quantization; Berezin-Toeplitz quantization; Berezin quantization; coherent state quantization; QUANTUM RIEMANN SURFACES; COHERENT-STATE REPRESENTATIONS; BEREZIN-TOEPLITZ QUANTIZATION; WEIGHTED BERGMAN KERNELS; PHASE-SPACE REDUCTION; DEFORMATION QUANTIZATION; GEOMETRIC-QUANTIZATION; KAHLER-MANIFOLDS; SYMPLECTIC-MANIFOLDS; HARMONIC-ANALYSIS;

Quantization methods: A guide for physicists and analysts

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