Quantum fluctuations of a "constant" gauge field

TL;DR

This paper investigates the quantum fluctuations of a rank-three gauge field, revealing its role in vacuum polarization, its association with the bag constant and cosmological term, and its Casimir-like effects on confinement and potential calculations.

Contribution

It introduces the unique properties of the A_{μνρ} gauge field, linking it to vacuum pressure, the bag constant, and the cosmological term, and calculates its effects on confinement and potential.

Findings

Quantum fluctuations are inversely proportional to confinement volume.

The field's fluctuations produce a Casimir effect for the vacuum.

The static potential is proportional to the enclosed volume.

Abstract

It is argued here that the quantum computation of the vacuum pressure must take into account the contribution of zero-point oscillations of a rank-three gauge field. The field A_{\mu\nu\rho} possesses no radiative degrees of freedom, its sole function being that of polarizing the vacuum through the formation of \textit{finite} domains characterized by a non-vanishing, constant, but otherwise arbitrary pressure. This extraordinary feature, rather unique among quantum fields, is exploited to associate the A_{\mu\nu\rho} field with the ``bag constant'' of the hadronic vacuum, or with the cosmological term in the cosmic case. We find that the quantum fluctuations of A_{\mu\nu\rho} are inversely proportional to the confinement volume and interpret the result as a Casimir effect for the hadronic vacuum. With these results in hands and by analogy with the electromagnetic and string case, we proceed to calculate the Wilson loop of the three-index potential coupled to a ``test'' relativistic bubble. From this calculation we extract the static potential between two opposite points on the surface of a spherical bag and find it to be proportional to the enclosed volume.