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 Aμνρ 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 Aμνρ 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 Aμνρ 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.