Canonical quantization and quantum chromodynamics in a cavity

Abstract

The canonical quantization formalism is applied to the Lagrange density of chromodynamics in a general covariant gauge. The physical states are characterized by their BRS-invariance. 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. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon and ghost field operators, the linear boundary conditions of the M.I.T. bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all non-divergent Feynman diagrams of second order in the strong coupling constant g. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.