English

The geometry of variations in Batalin-Vilkovisky formalism

Mathematical Physics 2013-12-05 v1 High Energy Physics - Theory Differential Geometry math.MP

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 "δ(0)=0\delta(0)=0" and "logδ(0)=0\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 δ\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).

Keywords

Cite

@article{arxiv.1312.1262,
  title  = {The geometry of variations in Batalin-Vilkovisky formalism},
  author = {Arthemy V. Kiselev},
  journal= {arXiv preprint arXiv:1312.1262},
  year   = {2013}
}

Comments

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