Lorentz-Covariant Quantization of Massive Non-Abelian Gauge Fields in The Hamiltonian Path-Integral Formalism

TL;DR

This paper presents a Lorentz-covariant Hamiltonian path-integral quantization method for massive non-Abelian gauge fields, ensuring consistency with the Lagrangian approach and incorporating the Lorentz condition as a constraint.

Contribution

It introduces a novel Hamiltonian path-integral formalism for massive non-Abelian gauge fields that maintains Lorentz covariance and aligns with the Faddeev-Popov method.

Findings

Quantization is Lorentz-covariant and consistent with Lagrangian formalism.

The Lorentz condition is effectively incorporated via Lagrange multipliers.

The approach confirms equivalence with established Faddeev-Popov quantization.

Abstract

The massive non-Abelian gauge fields are quantized Lorentz-covariantly in the Hamiltonian path-integral formalism. In the quantization, the Lorentz condition, as a necessary constraint, is introduced initially and incorporated into the massive Yang-Mills Lagrangian by the Lagrange multiplier method so as to make each temporal component of a vector potential to have a canonically conjugate counterpart. The result of this quantization is confirmed by the quantization performed in the Lagrangian path-integral formalism by applying the Lagrange multiplier method which is shown to be equivalent to the Faddeev-Popov approach.