Deformation stability of BRST quantization

Apr, 1998

Citations per year

19982000200220042006120
Abstract:
To avoid the problems which are connected with the long distance behavior of perturbative gauge theories we present a local construction of the observables which does not involve the adiabatic limit. First we construct the interacting fields as formal power series by means of causal perturbation theory. The observables are defined by BRST invariance where the BRST-transformation s~\tilde s acts as a graded derivation on the algebra of interacting fields. Positivity, i.e. the existence of Hilbert space representations of the local algebras of observables is shown with the help of a local Kugo-Ojima operator QintQ_{\rm int} which implements s~\tilde s on a local algebra and differs from the corresponding operator QQ of the free theory. We prove that the Hilbert space structure present in the free case is stable under perturbations. All assumptions are shown to be satisfied in QED in a finite spatial volume with suitable boundary conditions. As a by-product we find that the BRST-quantization is not compatible with periodic boundary conditions for massless free gauge fields.
  • quantum field theory
  • nonlinear field theory
  • gauge field theory
  • perturbation theory
  • Hilbert spaces
  • quantum electrodynamics
  • talk: Lodz 1998/04/15
  • gauge field theory: Yang-Mills
  • axiomatic field theory
  • field theory: deformation