# Resources on BRST and BV quantisation for local quantum field theories

This is a reference request, to ideally a textbook, monograph, set of lecture notes or lecture videos, on the topics of BRST quantisation and the Lagrangian BV formalism. My constraints are as follows:

1. Minimal use of the path integral formulation when possible, and minimal use of the category theoretical constructions of quantum field theory.
2. Described in the context of local quantum field theory, or provides examples in such a context in $$d \geq 2$$.

While not mandatory, I would appreciate if the resource referenced or used the viewpoint of gauge theory in terms of principal bundles and their associated vector bundles.

The resource may assume a strong background in the usual physics preliminaries, and a strong background in differential geometry, algebraic geometry, commutative algebra and homological algebra.

Resources I have already considered are:

• Aiming for minimal use of path integrals is probably a counterproductive restriction. A short presentation of the BV formalism for toy models given by finite dimensional path integrals is in the JMP article by Albert, Bleile and Froehlich aip.scitation.org/doi/full/10.1063/1.3278524 Jun 17 '20 at 14:31
• Other references that might be useful are the books Kasia Rejzner link.springer.com/book/10.1007/978-3-319-25901-7 and the one by Costello bookstore.ams.org/surv-170 Jun 17 '20 at 14:33
• @AbdelmalekAbdesselam If I loosened the path integral restriction, what would you recommend? Jun 17 '20 at 18:34
• The ones I just gave. I assumed loosening of the path integral restriction already. Jun 17 '20 at 21:09