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BV Quantization

Alberto S. Cattaneo, Pavel Mnev, Michele Schiavina

Abstract

This note gives an overview of the BV formalism in its various incarnations and applications.

BV Quantization

Abstract

This note gives an overview of the BV formalism in its various incarnations and applications.
Paper Structure (16 sections, 3 theorems, 49 equations)

This paper contains 16 sections, 3 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. BV quantization: the idea
  3. Zinn-Justin's effective action
  4. Geometric interpretation of the BV formalism
  5. BV algebras
  6. Canonical BV Laplacian on half-den-sities
  7. BV fiber integrals
  8. Solutions of the master equation and cyclic $L_\infty$ algebras.
  9. Field theory
  10. Locality, and infinite-dimen-sional geometry
  11. Infinite-dimen-sional BV formalism
  12. The AKSZ construction
  13. Effective regularization
  14. Time ordering and BV Laplacians
  15. Field theory on manifolds with boundary
  16. ...and 1 more sections

Key Result

Theorem 3.2

Theorems & Definitions (18)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Remark 2.5
  • Example 2.6
  • Remark 2.7
  • Remark 3.1
  • Theorem 3.2: Schwarz
  • Remark 3.3
  • ...and 8 more