One-loop Feynman diagram zeta functions for toroidal spacetime

Abstract

In field theory on the spacetime En*TN with partial toroidal compactification, a zeta function can be associated with any one-loop Feynman diagram having any number of external lines. This zeta function is a versatile field-theoretic tool. If a one-loop diagram is ultraviolet divergent, its zeta function will regularise this divergence. The real power of the diagram zeta function lies, however, in its ability to provide an exact power series expansion, in mass and external momentum, of its (regularised) diagram. New results are presented for field theory on En*TN using this method. Scalar and fermion one-loop vacuum diagrams and effective potentials are calculated. The attachment of external lines to the quantum loop is illustrated by a self-energy diagram computation. Topological mass generation in gauge theories due to toroidal compactification is investigated.