BRST Hamiltonian for Bulk-Quantized Gauge Theory

TL;DR

This paper develops a BRST Hamiltonian framework for bulk-quantized Yang-Mills theory, linking it to the Fokker-Planck equation and confirming consistency with the 5-dimensional Lagrangian formulation.

Contribution

It provides a new Hamiltonian derivation of the bulk action and connects the ground state to the Fokker-Planck equation, ensuring consistency with existing formulations.

Findings

Ground state is ghost-independent and solves the Fokker-Planck equation.

Vacuum correlators match those from the 5D Lagrangian approach.

Propagators remain parabolic at one-loop in dimensional regularization.

Abstract

By treating the bulk-quantized Yang-Mills theory as a constrained system we obtain a consistent gauge-fixed BRST hamiltonian in the minimal sector. This provides an independent derivation of the 5-d lagrangian bulk action. The ground state is independent of the (anti)ghosts and is interpreted as the solution of the Fokker-Planck equation, thus establishing a direct connection to the Fokker-Planck hamiltonian. The vacuum state correlators are shown to be in agreement with correlators in lagrangian 5-d formulation. It is verified that the complete propagators remain parabolic in one-loop dimensional regularization.