Quantum effects of a massive 3-form coupled to a Dirac field

TL;DR

This paper investigates the quantum effects of a massive 3-form field coupled to a Dirac spinor, revealing its impact on the effective dynamics, vacuum pressure, and confining properties of the system.

Contribution

It introduces a consistent framework for a massive 3-form field coupled to matter, analyzing its quantum fluctuations and gauge invariance, and explores its physical implications.

Findings

Mass term acts as an infrared cutoff in the vacuum pressure.

A_{μνρ} contains a mixture of massless and massive spin-0 fields.

The system exhibits gauge invariance and confinement properties.

Abstract

We consider the coupling of A_{\mu\nu\rho} to the generic current of matter field, later identified with the spin density current of a Dirac field. In fact, one of the objectives of this paper is to investigate the impact of the quantum fluctuations of A_{\mu\nu\rho} on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for A_{\mu\nu\rho}. In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of A_{\mu\nu\rho} and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, A_{\mu\nu\rho} contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of A_{\mu\nu\rho} since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of A_{\mu\nu\rho} already expected from the earlier calculation of the Wilson loop.