48 research outputs found
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
Perturbative gauge invariance: electroweak theory II
A recent construction of the electroweak theory, based on perturbative
quantum gauge invariance alone, is extended to the case of more generations of
fermions with arbitrary mixing. The conditions implied by second order gauge
invariance lead to an isolated solution for the fermionic couplings in
agreement with the standard model. Third order gauge invariance determines the
Higgs potential. The resulting massive gauge theory is manifestly gauge
invariant, after construction.Comment: 16 pages, latex, no figure
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
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
Protecting the conformal symmetry via bulk renormalization on Anti deSitter space
The problem of perturbative breakdown of conformal symmetry can be avoided,
if a conformally covariant quantum field phi on d-dimensional Minkowski
spacetime is viewed as the boundary limit of a quantum field Phi on
d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in
renormalized perturbation theory with polynomial interactions in AdS, and point
out the differences as compared to renormalization directly on the boundary. In
particular, provided the limit exists, there is no conformal anomaly. We
compute explicitly the "fish diagram" on AdS_4 by differential renormalization,
and calculate the anomalous dimension of the composite boundary field phi^2
with bulk interaction Phi^4.Comment: 40 page
Massive Vector Mesons and Gauge Theory
We show that the requirements of renormalizability and physical consistency
imposed on perturbative interactions of massive vector mesons fix the theory
essentially uniquely. In particular physical consistency demands the presence
of at least one additional physical degree of freedom which was not part of the
originally required physical particle content. In its simplest realization
(probably the only one) these are scalar fields as envisaged by Higgs but in
the present formulation without the ``symmetry-breaking Higgs condensate''. The
final result agrees precisely with the usual quantization of a classical gauge
theory by means of the Higgs mechanism. Our method proves an old conjecture of
Cornwall, Levin and Tiktopoulos stating that the renormalization and
consistency requirements of spin=1 particles lead to the gauge theory structure
(i.e. a kind of inverse of 't Hooft's famous renormalizability proof in
quantized gauge theories) which was based on the on-shell unitarity of the
-matrix. We also speculate on a possible future ghostfree formulation which
avoids ''field coordinates'' altogether and is expected to reconcile the
on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.
-algebraic approach to interacting quantum field theory: Inclusion of Fermi fields
We extend the -algebraic approach to interacting quantum field theory,
proposed recently by Detlev Buchholz and one of us (KF) to Fermi fields. The
crucial feature of our approach is the use of auxiliary Grassmann variables in
a functorial way.Comment: 31 pages, in this version we added a referenc