The geometry of variations in Batalin_Vilkovisky formalism

21st International Conference on Integrable Systems and Quantum Symmetries

Kiselev, Arthemy V.^1

Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, PO Box 407, 9700 AK Groningen, Netherlands^1

关键词: Cohomology;    Dirac's delta function;    Gauge symmetries;    Gauge systems;    Laplacians;    Quantisation;    Quantum master equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012024/pdf
DOI  :  10.1088/1742-6596/474/1/012024

来源: IOP

【 摘 要 】

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" and "log δ(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-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).