Cavity quantum chromodynamics

We develop practical and rigorous techniques for calculating and renormalizing loop diagrams in quantum chromodynamics defined in a static spherical cavity. Working with Feynman propagators and in the Feynman gauge, we use multiple-reflection expansions for the cavity propagators to isolate and analyze the short-distance singularities in graphs. Nonsingular contributions to graphs are evaluated using a set of "Feynman rules" in an energy—angular-momentum representation. As an application we describe the calculation of the quark self-energy to lowest order in ${\alpha }_s$. We show that the self-energy of a confined massless quark is finite and unambiguous, and that all divergences in the case of a massive quark can be absorbed into a state-independent mass renormalization just as in free space.