Quantum effects of a massive three form coupled to a Dirac field.

The computation of the quantum vacuum pressure must take into account the contribution of zero-point oscillations of a rank-three gauge field Aμνρ. This result was established in a previous paper where we calculated both the Casimir pressure within a region of vacuum simulating a hadronic bag and the Wilson factor for the three-index potential associated with the boundary of the bag. The resulting “volume law” satisfied by the Wilson loop is consistent with the basic confining requirement that the static interquark potential increases with the distance between two test charges. As a sequel to that paper, we consider here the coupling of Aμνρ to the generic current of a 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 Aμνρ on the effective dynamics of the spinor field.