Abstract
The computation of the quantum vacuum pressure must take into account the contribution of zero-point oscillations of a rank-three gauge field 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 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 on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of already expected from the earlier calculation of the Wilson loop.
- Received 14 August 2003
DOI:https://doi.org/10.1103/PhysRevD.69.105005
©2004 American Physical Society