A new massive vector field theory

TL;DR

This paper introduces a novel massive spin-1 vector field theory with a natural quantization approach, explores its Lorentz invariance, develops a corresponding vector QED, and demonstrates its renormalizability without Higgs mechanism, with concrete calculations of polarization cross sections.

Contribution

It presents a new massive vector field theory with a unique quantization method and establishes a renormalizable vector QED without Higgs mechanism, differing from traditional models.

Findings

The new vector field theory is Lorentz invariant with a special meaning.

Vector QED based on the new field is manifestly renormalizable.

Polarization cross section for $e^+ e^- o f^+ f^-$ is nearly zero with longitudinal momenta.

Abstract

In this paper, we put forth a new massive spin-1 field theory. In contrast to the quantization of traditional vector field, the quantization of the new vector field is carried out in a natural way. The Lorentz invariance of the theory is discussed, where owing to an interesting feature of the new vector field, the Lorentz invariance has a special meaning. In term of formalism analogical to QED(i. e. spinor QED), we develop the quantum electrodynamics concerning the new spin-1 particles, say, vector QED, where the Feynman rules are given. The renormalizability of vector QED is manifest without the aid of Higgs mechanism. As an example, the polarization cross section $\sigma_{polar}$ for $e^+ e^-\to f^+ f^-$ is calculated in the lowest order. It turns out that $\sigma_{polar}\sim 0$ and the momentum of $f^+$ and $f^-$ is purely longitudinal.