In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov's method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this
โฆ LIBER โฆ
Quantization based on generalized Poisson brackets
โ Scribed by C. C. Yan
- Book ID
- 112835339
- Publisher
- Springer-Verlag,Italian Physical Society
- Year
- 1992
- Weight
- 966 KB
- Volume
- 107
- Category
- Article
- ISSN
- 0369-3554
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Poisson brackets (P.b.) are the natural initial terms for the deformation quantization of commutative algebras. There is an open problem whether any Poisson bracket on the polynomial algebra of n variables can be quantized. It is known (Poincare-Birkhoff-Witt theorem) that any linear P.b. for all n