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:
- Minimal use of the path integral formulation when possible, and minimal use of the category theoretical constructions of quantum field theory.
- 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:
- Quantisation of Gauge Systems by Hennaux et al, a very comprehensive book but difficult to distil what is essential and what can be ignored, depending on requirements. Large dependency on previous chapters. Very encyclopaedic.
- Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications by Mnev (or his notes). Maybe the best resource I know of, but rather concise.
- Miscellaneous chapters in books like BBS's String Theory and M-Theory offer an introduction to the BRST formalism, but lack some mathematical generality I would enjoy, and the references to cohomology are brief, à la physicists.