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Quantum fluctuations of a "constant" gauge field

A. Aurilia·E. Spallucci
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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_{μνρ} 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_{μνρ} 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_{μνρ} 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.

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A. Aurilia, E. Spallucci. 2004-02-12. Quantum fluctuations of a "constant" gauge field. https://doi.org/10.1103/physrevd.69.105004

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