1,042 research outputs found
Deformation stability of BRST-quantization
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
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
which implements on a local algebra and differs from
the corresponding operator 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.Comment: 10 pages, the paper is written by means of LATEX, some macros are at
the beginning of the fil
Metric- and frame-like higher-spin gauge theories in three dimensions
We study the relation between the frame-like and metric-like formulation of
higher-spin gauge theories in three space-time dimensions. We concentrate on
the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the
frame-like formulation. The metric-like theory is obtained by eliminating the
generalised spin connection by its equation of motion, and by expressing
everything in terms of the metric and a spin-3 Fronsdal field. We give an exact
map between fields and gauge parameters in both formulations. To work out the
gauge transformations explicitly in terms of metric-like variables, we have to
make a perturbative expansion in the spin-3 field. We describe an algorithm how
to do this systematically, and we work out the gauge transformations to cubic
order in the spin-3 field. We use these results to determine the gauge algebra
to this order, and explain why the commutator of two spin-3 transformations
only closes on-shell.Comment: 26 pages, no figure
On boundary RG-flows in coset conformal field theories
We propose a new rule for boundary renormalization group flows in fixed-point
free coset models. Our proposal generalizes the 'absorption of boundary
spin'-principle formulated by Affleck and Ludwig to a large class of
perturbations in boundary conformal field theories. We illustrate the rule in
the case of unitary minimal models.Comment: 3 pages, uses RevTeX
Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
We present a perturbative construction of interacting quantum field theories
on any smooth globally hyperbolic manifold. We develop a purely local version
of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using
techniques from microlocal analysis. As byproducts, we describe a perturbative
construction of local algebras of observables, present a new definition of Wick
polynomials as operator-valued distributions on a natural domain, and we find a
general method for the extension of distributions which were defined on the
complement of some surfaces.Comment: 38 pages, LaTeX with AMSLaTeX style option, Micro.tex macrofil
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