Geometrical effective action: Gauge field theory without ghosts.

摘要

Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph.;Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions;Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show that ghosts are in fact not needed, even in a manifestly covariant quantum theory, and that a gauge invariant quantum effective action can be introduced which, like the classical action from which one starts, is independent of ghosts and gauge-breaking terms.;In this dissertation a quantum effective action for gauge field theories is constructed that is gauge invariant and independent of the choice of gauge breaking terms in the functional integral that defines it. The loop expansion of this effective action leads to new Feynman rules, involving new vertex functions but without diagrams containing ghost lines. The new rules are given in full for the Yang-Mills field, both with and without coupling to fermions, and renormalization procedures are described. No BRST arguments are needed. (Abstract shortened by UMI.) ftn