Free Energy of a Four-Dimensional Chiral Bag

Through the application of mathematical methods developed in a recent paper, we obtain a closed expression for the chiral correction to the free energy of a bag, due to the presence of the external pionic field in a hedgehog configuration. Low and high temperature developments are given and, in particular, the zero temperature limit is shown to be consistent with previous evaluations of the Casimir energy. The subject of renormalization is also discussed. Pacs: 12.40.Aa, 02.90.+p This work was partially supported by CONICET (Argentina). 1 Introduction It is by now a well-established fact that, when field configurations are subject to boundary conditions, their quantum fluctuations are modified in a fundamental way. Starting from the well-known work of Casimir [1], there has been ever growing evidence of the relevance of boundary effects on the vacuum structure of confined systems. One of the best illustrations of this fact is provided by bag models of hadrons, both in the early MI..