Massive Gauge Field Theory Without Higgs Mechanism I. .Quantization

TL;DR

This paper proposes a novel approach to quantize massive gauge fields without the Higgs mechanism by incorporating the Lorentz condition, maintaining gauge invariance and renormalizability.

Contribution

It introduces a gauge-invariant, renormalizable quantum gauge field theory with mass terms without relying on the Higgs mechanism, using BRST symmetry and Lorentz constraints.

Findings

The theory maintains gauge invariance with mass terms.

The approach ensures good renormalizability.

It provides a consistent quantization method for massive gauge fields.

Abstract

According to the conventional concept of the gauge field theory, the local gauge invariance excludes the possibility of giving a mass to the gauge boson without resorting to the Higgs mechanism because the Lagrangian constructed by adding a mass term to the Yang-Mills Lagrangian is not only gauge-non-invariant, but also unrenormalizable. On the contrary, we argue that the principle of gauge invariance actually allows a mass term to enter the Lagrangian if the Lorentz constraint condition is taken into account at the same time. The Lorentz condition, which implies vanishing of the unphysical longitudinal field, defines a gauge-invariant physical space for the massive gauge field. The quantum massive gauge field theory without Higgs mechanism may well be established by using a BRST-invariant action which is constructed by the Lagrange undetermined multiplier procedure of incorporating the Lorentz condition and another condition constraining the gauge group into the original massive Yang-Mills action. The quantum theory established in this way shows good renormalizability.