Quantum fluctuations of a “constant” gauge field

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 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.