Star Products: Their Ubiquity and Unicity

Sternheimer, Daniel

doi:10.1007/978-94-015-8543-9_23

Cited by 1 publication

(2 citation statements)

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“…We have not, for instance, at all touched the important and fairly complex problem of quantization with constraints, including BFV and BRST quantizations (see Sniatycki [232], Tuynman [244], Ibort [134], Batalin and Tyutin [27], Batalin, Fradkin and Fradkina [26], Kostant and Sternberg [158], Grigoriev and Lyakhovich [119]) and the relationship between quantization and reduction (Sjamaar [229], Tian and Zhang [239], Jorjadze [135], Bordemann, Herbig and Waldmann [44], Mladenov [173], Huebschmann [132], Vergne [255]); or quantum field theory and field quantization (Greiner and Reinhardt [118], Borcherds and Barnard [25]), etc. Some useful surveys concerning the topics we have covered, as well as some of those that we have not, are Sternheimer [237], Weinstein [260], Fernandes [89], Echeverria-Enriquez et al [78], Sniatycki [230], Ali [3], Blattner [38], Tuynman [245], Borthwick [48], and the books of Fedosov [88], Landsman [162], Bates and Weinstein [28], Souriau [233], Perelomov [203], Bandyopadhyay [21], Greiner and Reinhardt [118] and Woodhouse [263] mentioned above.…”

Section: Some Other Quantization Methodsmentioning

confidence: 99%

“…Some other nice articles on deformation quantization are Sternheimer [237], Arnal, Cortet, Flato and Sternheimer [19], Weinstein [260], Fernandes [89], and Blattner [38]; two recent survey papers are Gutt [125] and Dito and Sternheimer [74]. See also Neumaier [185], Bordemann and Waldmann [46], Karabegov [138] [140], Duval, Gradechi and Ovsienko [77], and the above mentioned books by Fedosov [88] and Landsman [162] and papers by Rieffel [215] [217].…”

Section: Deformation Quantizationmentioning

confidence: 99%

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Quantization Methods: A Guide for Physicists and Analysts

2005

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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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