382 research outputs found
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
Regularization in quantum field theory from the causal point of view
The causal approach to perturbative quantum field theory is presented in
detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko
Glaser in 1973. Causal perturbation theory is a mathematically rigorous
approach to renormalization theory, which makes it possible to put the
theoretical setup of perturbative quantum field theory on a sound mathematical
basis. Epstein and Glaser solved this problem for a special class of
distributions, the time-ordered products, that fulfill a causality condition,
which itself is a basic requirement in axiomatic quantum field theory. In their
original work, Epstein and Glaser studied only theories involving scalar
particles. In this review, the extension of the method to theories with higher
spin, including gravity, is presented. Furthermore, specific examples are
presented in order to highlight the technical differences between the causal
method and other regularization methods, like, e.g. dimensional regularization.Comment: 75 pages, 8 figures, style file included, some comments and
references adde
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
Two-Loop Diagrams in Causal Perturbation Theory
The scalar two-loop master diagram is revisited in the massive cases needed
for the computation of boson and fermion propagators in QED and QCD. By means
of the causal method it is possible in a straightforward manner to express the
propagators as double integrals. In the case of vacuum polarization both
integrations can be carried out in terms of polylogarithms, whereas the last
integral in the fermion propagator cannot be expressed by known special
functions. The advantage of the method in comparison with Feynman integral
calculations is indicated.Comment: 16 pages, latex, the figures can be ordered at the first authors
address (A.Aste), the necessary macros are included in the latex-fil
Quantum field theory meets Hopf algebra
This paper provides a primer in quantum field theory (QFT) based on Hopf
algebra and describes new Hopf algebraic constructions inspired by QFT
concepts. The following QFT concepts are introduced: chronological products,
S-matrix, Feynman diagrams, connected diagrams, Green functions,
renormalization. The use of Hopf algebra for their definition allows for simple
recursive derivations and lead to a correspondence between Feynman diagrams and
semi-standard Young tableaux. Reciprocally, these concepts are used as models
to derive Hopf algebraic constructions such as a connected coregular action or
a group structure on the linear maps from S(V) to V. In most cases,
noncommutative analogues are derived.Comment: 27 pages, 4 figures. Slightly edited version of the published pape
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