Off-shell Gauge Fields from BRST Quantization
Maxim Grigoriev
TL;DR
This work presents a unified framework to construct nonlinear off-shell gauge theories from quantum constrained systems by interpreting the star-product BFV–BRST master equation as the equations of motion. By coupling BRST-extended unfolded formalisms with AKSZ/Fedosov quantization, it derives linear and nonlinear descriptions of off-shell higher-spin fields on Minkowski and AdS backgrounds, including explicit trace constraints via BRST cohomology and auxiliary fields. The approach yields a parent-form perspective that links to Fronsdal HS theory, provides AdS embedding-space formulations, and identifies topological HS sectors through cohomological reductions. Overall, the framework offers a geometrically transparent, BRST-based route to off-shell HS dynamics across flat and curved spacetimes with a clear path to interactions via the unfolded/AKSZ viewpoint.
Abstract
We propose a construction for nonlinear off-shell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the star-product BFV--BRST master equation as an equation of motion. The construction is formulated in terms of the BRST extention of the unfolded formalism that can also be understood as an appropriate generalization of the AKSZ procedure. As an application, we consider a very simple constrained system, a quantized scalar particle, and show that it gives rise to an off-shell higher-spin gauge theory that automatically appears in the parent form and properly takes the familiar trace constraint into account. In particular, we derive a geometrically transparent form of the off-shell higher-spin theory on the AdS background.