Quantization of The Electroweak Theory in The Hamiltonian Path-Integral Formalism

TL;DR

This paper develops a Hamiltonian path-integral quantization method for the electroweak theory, incorporating gauge constraints to achieve Lorentz covariance, aligning with the Faddeev-Popov approach.

Contribution

It introduces a Hamiltonian path-integral formalism for electroweak theory that effectively handles gauge constraints and reproduces known covariant quantization results.

Findings

Achieves Lorentz-covariant quantization in Hamiltonian formalism.

Shows equivalence with Faddeev-Popov quantization.

Handles unphysical gauge components systematically.

Abstract

The quantization of the SU(2)$\times $U(1) gauge-symmetric electroweak theory is performed in the Hamiltonian path-integral formalism. In this quantization, we start from the Lagrangian given in the unitary gauge in which the unphysical Goldstone fields are absent, but the unphysical longitudinal components of the gauge fields still exist. In order to eliminate the longitudinal components, it is necessary to introduce the Lorentz gauge conditions as constraints. These constraints may be incorporated into the Lagrangian by the Lagrange undetermined multiplier method. In this way, it is found that every component of a four-dimensional vector potential has a conjugate counterpart. Thus, a Lorentz-covariant quantization in the Hamiltonian path-integral formalism can be well accomplished and leads to a result which is the same as given by the Faddeev-Popov approach of quantization.