  In this paper the connection between standard perturbation theory techniques
and the new Bern-Kosower calculational rules for gauge theory is clarified. For
one-loop effective actions of scalars, Dirac spinors, and vector bosons in a
background gauge field, Bern-Kosower-type rules are derived without the use of
either string theory or Feynman diagrams. The effective action is written as a
one-dimensional path integral, which can be calculated to any order in the
gauge coupling; evaluation leads to Feynman parameter integrals directly,
bypassing the usual algebra required from Feynman diagrams, and leading to
compact and organized expressions. This formalism is valid off-shell, is
explicitly gauge invariant, and can be extended to a number of other field
theories.
