A note on the existence of graded extensions of Poisson brackets
โ Scribed by L.A. Ibort; J. Monterde
- Book ID
- 108006964
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 379 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0393-0440
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๐ SIMILAR VOLUMES
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
We extend the Poisson bracket from a Lie bracket of phase space functions to a Lie bracket of functions on the space of canonical histories and investigate the resulting algebras. Typically, such extensions define corresponding Lie algebras on the space of Lagrangian histories via pullback to a spac