The BRST complex of homological Poisson reduction. (English) Zbl 1375.17015
Summary: BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal \(J\) of a Poisson algebra \(P\) and provide a description of the Poisson algebra \((P/J)^J\) as their cohomology in degree zero. Using the notion of stable equivalence introduced in [G. Felder and D. Kazhdan, Contemp. Math. 610, 79–137 (2014; Zbl 1304.81144)], we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case \(P = \mathbb R[V]\) where \(V\) is a finite-dimensional symplectic vector space and the bracket on \(P\) is induced by the symplectic structure on \(V\). As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal \(J\) in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal \(J\). We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the
quantization procedure.
MSC:
| 17B63 | Poisson algebras |
| 17B55 | Homological methods in Lie (super)algebras |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T70 | Quantization in field theory; cohomological methods |
| 81S22 | Open systems, reduced dynamics, master equations, decoherence |
Citations:
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