The geometry of variations in Batalin-Vilkovisky formalism

Abstract

This is a paper about geometry of (iterated) variations. We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "$\delta (0)=0$" and "$\log \delta (0)=0$" within BV-approach to quantisation of gauge systems. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's $\delta$-function as a limit of smooth kernels. We illustrate the reasoning by re-deriving - but not just "formally postulating" - the standard properties of BV-Laplacian and Schouten bracket and by verifying their basic inter-relations (e.g., cohomology preservation by gauge symmetries of the quantum master-equation).

XXI International Conference on Integrable Systems and Quantum Symmetries (ISQS21) 11-16 June 2013 at CVUT Prague, Czech Republic; 51 pages (9 figures). - Main Example 2.4 on pp.34-36 retained from arXiv:1302.4388v1, standard proofs in Appendix A amended and quoted from arXiv:1302.4388v1 (joint with S.Ringers). - Solution to Exercise 11.6 from IHES/M/12/13 by the same author

References in corpus (2)

• Renormalisation and the Batalin-Vilkovisky formalism
• On the geometry of the Batalin-Vilkovisky Laplacian

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• The expansion $\star$ mod $\bar{o}({\hslash }^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization
• The right-hand side of the Jacobi identity: to be naught or not to be?