|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
18 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Fedosov Deformation Quantization as a BRST Theory | | M.A. Grigoriev
; S.L. Lyakhovich
; | | Date: |
14 Mar 2000 | | Journal: | Commun.Math.Phys. 218 (2001) 437-457 | | Subject: | High Energy Physics - Theory; Quantum Algebra; Differential Geometry | hep-th math.DG math.QA | | Abstract: | The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold $mathcal M$ is presented as a second class constrained surface in the fibre bundle ${{mathcal T}^*_
ho}{mathcal M}$ which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ${{mathcal T}^*_
ho}{mathcal M}$ and the tangent bundle $T {mathcal M}$. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables. | | Source: | arXiv, hep-th/0003114 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER