BV equivalence with boundary

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.