173 research outputs found
Slavnov-Taylor Identities from the Causal Point of View
We continue the investigation of quantized Yang-Mills theories coupled to
matter fields in the framework of causal perturbation theory which goes back to
Epstein and Glaser. In this approach gauge invariance is expressed by a simple
commutator relation for the S-matrix and the corresponding gauge
transformations are simple transformations of the free fields only. In spite of
this simplicity, gauge invariance implies the usual Slavnov-Taylor identities.
The main purpose of this paper is to prove the latter statement. Since the
Slavnov-Taylor identities are formulated in terms of Green's functions, we
investigate the agreement of two perturbative definitions of Green's functions,
namely of Epstein and Glaser's definition with the Gell-Mann Low series.Comment: 29 pages. The paper is written in TEX. The necessary macros are
included. The figures are not done by computer, they can be ordered at the
authors addres
A local (perturbative) construction of observables in gauge theories: the example of QED
Interacting fields can be constructed as formal power series in the framework
of causal perturbation theory. The local field algebra is obtained without performing the adiabatic limit; the (usually bad)
infrared behavior plays no role. To construct the observables in gauge theories
we use the Kugo-Ojima formalism; we define the BRST-transformation
as a graded derivation on the algebra of interacting fields and use the
implementation of by the Kugo-Ojima operator . Since
our treatment is local, the operator 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.Comment: corrected typos, a few supplements, 34 pages, written by TEX, some
macros are at the beginning of the file. To appear in Commun. Math. Phy
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
The Master Ward Identity
In the framework of perturbative quantum field theory (QFT) we propose a new,
universal (re)normalization condition (called 'master Ward identity') which
expresses the symmetries of the underlying classical theory. It implies for
example the field equations, energy-momentum, charge- and ghost-number
conservation, renormalized equal-time commutation relations and BRST-symmetry.
It seems that the master Ward identity can nearly always be satisfied, the
only exceptions we know are the usual anomalies. We prove the compatibility of
the master Ward identity with the other (re)normalization conditions of causal
perturbation theory, and for pure massive theories we show that the 'central
solution' of Epstein and Glaser fulfills the master Ward identity, if the
UV-scaling behavior of its individual terms is not relatively lowered.
Application of the master Ward identity to the BRST-current of non-Abelian
gauge theories generates an identity (called 'master BRST-identity') which
contains the information which is needed for a local construction of the
algebra of observables, i.e. the elimination of the unphysical fields and the
construction of physical states in the presence of an adiabatically switched
off interaction.Comment: 73 pages, version to appear in Rev. Math. Phy
Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
The perturbative treatment of quantum field theory is formulated within the
framework of algebraic quantum field theory. We show that the algebra of
interacting fields is additive, i.e. fully determined by its subalgebras
associated to arbitrary small subregions of Minkowski space. We also give an
algebraic formulation of the loop expansion by introducing a projective system
of observables ``up to loops'' where is
the Poisson algebra of the classical field theory. Finally we give a local
algebraic formulation for two cases of the quantum action principle and compare
it with the usual formulation in terms of Green's functions.Comment: 29 page
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