466 research outputs found
Gauge invariance of massless QED
A simple general proof of gauge invariance in QED is given in the framework
of causal perturbation theory. It illustrates a method which can also be used
in non-abelian gauge theories.Comment: 7 pages, TEX-file, Zuerich University Preprint ZU-TH-33/199
The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
In the framework of perturbative quantum field theory a new, universal
renormalization condition (called Master Ward Identity) was recently proposed
by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the
present paper is to get a better understanding of the Master Ward Identity by
analyzing its meaning in classical field theory. It turns out that it is the
most general identity for classical local fields which follows from the field
equations. It is equivalent to a generalization of the Schwinger-Dyson Equation
and is closely related to the Quantum Action Principle of Lowenstein and Lam.
As a byproduct we give a self-contained treatment of Peierls' manifestly
covariant definition of the Poisson bracket.Comment: 56 pages. to appear in Commun. Math. Phy
Non-Uniqueness of Quantized Yang-Mills Theories
We consider quantized Yang-Mills theories 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.
The most general coupling which is gauge invariant in first order contains a
two-parametric ambiguity in the ghost sector - a divergence- and a
coboundary-coupling may be added. We prove (not completely) that the higher
orders with these two additional couplings are gauge invariant, too. Moreover
we show that the ambiguities of the n-point distributions restricted to the
physical subspace are only a sum of divergences (in the sense of vector
analysis). It turns out that the theory without divergence- and
coboundary-coupling is the most simple one in a quite technical sense. The
proofs for the n-point distributions containing coboundary-couplings are given
up to third or fourth order only, whereas the statements about the
divergence-coupling are proven in all orders.Comment: 22 pages. The paper is written in TEX. The necessary macros are
include
Comments on the Gauge Fixed BRST Cohomology and the Quantum Noether Method
We discuss in detail the relation between the gauge fixed and gauge invariant
BRST cohomology. We showed previously that in certain gauges some cohomology
classes of the gauge-fixed BRST differential do not correspond to gauge
invariant observables. We now show that in addition ``accidental'' conserved
currents may appear. These correspond one-to-one to observables that become
trivial in this gauge. We explicitly show how the gauge-fixed BRST cohomology
appears in the context of the Quantum Noether Method.Comment: 24 pages, example section improved, short version without background
material will appear in Physics Letters
General massive gauge theory
The concept of perturbative gauge invariance formulated exclusively by means
of asymptotic fields is used to construct massive gauge theories. We consider
the interactions of massive and massless gauge fields together with
fermionic ghost and anti-ghost fields. First order gauge invariance
requires the introduction of unphysical scalars (Goldstone bosons) and fixes
their trilinear couplings. At second order additional physical scalars (Higgs
fields) are necessary, their coupling is further restricted at third order. In
case of one physical scalar all couplings are determined by gauge invariance,
including the Higgs potential. For three massive and one massless gauge field
the electroweak theory comes out as the unique solution.Comment: 20 pages, latex, no figure
The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
We complete our study of non-Abelian gauge theories in the framework of
Epstein-Glaser approach to renormalization theory including in the model an
arbitrary number of Dirac Fermions. We consider the consistency of the model up
to the third order of the perturbation theory. In the second order we obtain
pure group theoretical relations expressing a representation property of the
numerical coefficients appearing in the left and right handed components of the
interaction Lagrangian. In the third order of the perturbation theory we obtain
the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate
Removal of violations of the Master Ward Identity in perturbative QFT
We study the appearance of anomalies of the Master Ward Identity, which is a
universal renormalization condition in perturbative QFT. The main insight of
the present paper is that any violation of the Master Ward Identity can be
expressed as a LOCAL interacting field; this is a version of the well-known
Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field
formalism by induction on the order in , this knowledge about the
structure of possible anomalies as well as techniques of algebraic
renormalization are used to remove possible anomalies by finite
renormalizations. As an example the method is applied to prove the Ward
identities of the O(N) scalar field model.Comment: 51 pages. v2: a few formulations improved, one reference added. v3: a
few mistakes corrected and one additional reference. v4: version to be
printed in Reviews in Mathematical Physic
Perturbative quantum gauge invariance: Where the ghosts come from
A condensed introduction to quantum gauge theories is given in the
perturbative S-matrix framework; path integral methods are used nowhere. This
approach emphasizes the fact that it is not necessary to start from classical
gauge theories which are then subject to quantization, but it is also possible
to recover the classical group structure and coupling properties from purely
quantum mechanical principles. As a main tool we use a free field version of
the Becchi-Rouet-Stora-Tyutin gauge transformation, which contains no
interaction terms related to a coupling constant. This free gauge
transformation can be formulated in an analogous way for quantum
electrodynamics, Yang-Mills theories with massless or massive gauge bosons and
quantum gravity.Comment: 28 pages, LATEX. Some typos corrected, version to be publishe
On the assertion that PCT violation implies Lorentz non-invariance
Out of conviction or expediency, some current research programs take for
granted that "PCT violation implies violation of Lorentz invariance". We point
out that this claim is still on somewhat shaky ground. In fact, for many years
there has been no strengthening of the evidence in this direction. However,
using causal perturbation theory, we prove here that when starting with a local
PCT-invariant interaction, PCT symmetry can be maintained in the process of
renormalization.Comment: 13 page
On Gauge Invariance and Spontaneous Symmetry Breaking
We show how the widely used concept of spontaneous symmetry breaking can be
explained in causal perturbation theory by introducing a perturbative version
of quantum gauge invariance. Perturbative gauge invariance, formulated
exclusively by means of asymptotic fields, is discussed for the simple example
of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant
for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure
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