Classical BV theories on manifolds with boundary. (English) Zbl 1302.81141
Between 1977 and 1983 Batalin and Vilkovisky published a number of papers in which they studied gauge algebra in general and the quantization of theories with linearly dependent generators. The BV approach generalizes the Faddeev-Popov and the BRST methods. In their paper, Cattaneo et.al. reformulate the classical BV framework for gauge theories on spacetime manifolds with boundaries. They consider it as a first step towards a perturbative quantization of classical BV theories and so the ultimate goal is to construct topological invariants in the context of perturbation theory. Topological field theories such as the Chern-Simons theory and similar models are very particular: Feynman diagrams have no ultraviolet divergencies and the partition function is independent of the metric and therefore a topological invariant. Developing the perturbative Chern-Simons quantization for bounded manifolds is one of the main motivation for the project that Callaneo et.al. started in the present paper. Section 3 is the central part of this paper. Here they formulate the BV framework for gauge theories and propose an analogue of the classical master equation for bounded spacetime manifolds. They define moduli spaces and address the problem of gluing two manifolds together.
Reviewer: Gert Roepstorff (Aachen)
MSC:
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T45 | Topological field theories in quantum mechanics |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T70 | Quantization in field theory; cohomological methods |
Keywords:
gauge theory; spacetime manifolds with boundary; Batalin-Vilkovisky framework; perturbative quantization; Chern-Somons theory; moduli spaces; topological invariantsReferences:
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