Perturbative algebraic quantum field theory with smoothened boundary
arXiv:2607.13765
The paper develops a perturbative algebraic quantum field theory framework for gauge fields on globally hyperbolic Lorentzian manifolds with boundaries, using BV/BFV formalisms to define modified master equations and a renormalized quantum BFV operator, and shows that the resulting quantum homotopy dg Lie algebra acquires curvature due to the boundary.
Abstract
We formulate quantisation of gauge field theories on globally hyperbolic Lorentzian manifolds with marked hypersurfaces within the framework of perturbative algebraic quantum field theory (pAQFT) enriched by the Batalin, Fradkin, Vilkovisky formalism (BV/BFV). This allows one to incorporate some crucial aspects of the local functorial approach to gauge field theory on manifolds with boundary within the algebraic setting. In particular, we provide a pAQFT-formulation of the modified classical and quantum master equations (after Cattaneo, Mnev and Reshetikhin CMR), as well as a constructive way to build a renormalised quantum BFV operator correcting the failure of the Quantum Master Equation by means of boundary terms (in the appropriate sense). We find that the renormalised quantum homotopy dg Lie algebra arising from the Anomalous Master Ward Identity becomes curved when boundaries are considered. The failure of the quantum master equation is thus encoded by a nontrivial curvature term in an algebra. As a byproduct, we recover previous results of Hollands' on the relation between the (boundary) BRST charge and the BV operator, and we recover CMR's ansatz for the quantum BFV operator at leading perturbative order on causal cylinders in Abelian Yang--Mills theory.
62pp + refs