Exact Renormalized One-Loop Quantum Corrections to Energies of Solitonic Field Configurations

Abstract

We develop a method for computing exact one-loop quantum corrections to the energies of static classical backgrounds in renormalizable quantum field theories. We use a continuum density of states formalism to construct a regularized Casimir energy in terms of phase shifts and their Born approximations. This method unambiguously incorporates definite counterterms fixed in the standard way by physical renormalization conditions. The result is a robust computation that can be efficiently implemented both numerically and analytically. We carry out such calculations in models of bosons and fermions in one and three dimensions.

arXiv commentM.I.T. Ph.D thesis; 72 pages, uses mitthesis.sty; v2: fixed minor error in eq (B.22); v3: fixed minor error in eq. (4.57)