Canonical quantization and chromodynamics in a spherical cavity

Abstract

The canonical quantization formalism is applied to the Lagrange density of chromodynamics, which includes gauge fixing and Faddeev-Popov ghost terms in a general covariant gauge. We develop the quantum theory of the interacting fields in the Dirac picture, based on the Gell-Mann and Low theorem and the Dyson expansion of the time evolution operator. The physical states are characterized by their invariance under Becchi-Rouet-Stora transformations. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon, and ghost field operators, the linear boundary conditions of the MIT bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all nondivergent Feynman diagrams of second order in the strong coupling constantg. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.