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F M Castela Simão1, A S Cattaneo2, M Schiavina3,4

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Summary
This summary is machine-generated.

This study introduces strict and lax classical equivalence for local Lagrangian field theories within Batalin-Vilkovisky (BV) and BFV frameworks. Strict equivalence, crucial for quantization, refines notions of theory equivalence.

Keywords:
BFV formalismBV formalismClassical field theoryGauge theoryYang-Mills theory

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics

Background:

  • Classical equivalence is extended to Batalin-Vilkovisky (BV) and Batalin-Fradkin-Vilkovisky (BFV) frameworks for local Lagrangian field theories.
  • This framework applies to manifolds, including those with boundaries, which are essential for quantization.

Purpose of the Study:

  • To discuss an extension of classical equivalence in BV and BFV formalisms.
  • To distinguish between strict and lax senses of equivalence based on BV and boundary BFV data compatibility.
  • To analyze specific field theories under these equivalence notions.

Main Methods:

  • The study defines strict equivalence via compatible BV and boundary BFV data, necessary for quantization.
  • It examines first- and second-order formulations of nonabelian Yang-Mills and classical mechanics on curved backgrounds.
  • It compares Jacobi theory and 1D gravity with scalar matter as reparametrization-invariant classical mechanics.

Main Results:

  • First- and second-order Yang-Mills and classical mechanics are pairwise strictly equivalent as BV-BFV theories, implying quasi-isomorphic BV complexes.
  • Jacobi theory and 1D gravity are laxly equivalent, possessing isomorphic BV cohomologies.
  • Only 1D gravity with scalar matter admits a strict BV-BFV formulation.

Conclusions:

  • Strict BV-BFV equivalence is a more refined concept than lax equivalence.
  • The findings highlight the importance of strict equivalence for quantization in field theory.
  • This work clarifies the relationship between different formulations of physical theories within the BV-BFV framework.