2,115 research outputs found
Axial Anomaly from the BPHZ regularized BV master equation
A BPHZ renormalized form for the master equation of the field antifiled (or
BV) quantization has recently been proposed by De Jonghe, Paris and Troost.
This framework was shown to be very powerful in calculating gauge anomalies. We
show here that this equation can also be applied in order to calculate a global
anomaly (anomalous divergence of a classically conserved Noether current),
considering the case of QED. This way, the fundamental result about the
anomalous contribution to the Axial Ward identity in standard QED (where there
is no gauge anomaly) is reproduced in this BPHZ regularized BV framework.Comment: 10 pages, Latex, minor changes in the reference
THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL
Using the exact path integral solution of the Schwinger model -- a model
where instantons are present -- the Dyson-Schwinger equation is shown to hold
by explicit computation. It turns out that the Dyson-Schwinger equation
separately holds for every instanton sector. This is due to Theta-invariance of
the Schwinger model.Comment: LATEX file 11 pages, no figure
Gauge dependence of effective action and renormalization group functions in effective gauge theories
The Caswell-Wilczek analysis on the gauge dependence of the effective action
and the renormalization group functions in Yang-Mills theories is generalized
to generic, possibly power counting non renormalizable gauge theories. It is
shown that the physical coupling constants of the classical theory can be
redefined by gauge parameter dependent contributions of higher orders in
in such a way that the effective action depends trivially on the gauge
parameters, while suitably defined physical beta functions do not depend on
those parameters.Comment: 13 pages Latex file, additional comments in section
Approach to a rational rotation number in a piecewise isometric system
We study a parametric family of piecewise rotations of the torus, in the
limit in which the rotation number approaches the rational value 1/4. There is
a region of positive measure where the discontinuity set becomes dense in the
limit; we prove that in this region the area occupied by stable periodic orbits
remains positive. The main device is the construction of an induced map on a
domain with vanishing measure; this map is the product of two involutions, and
each involution preserves all its atoms. Dynamically, the composition of these
involutions represents linking together two sector maps; this dynamical system
features an orderly array of stable periodic orbits having a smooth parameter
dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure
On a class of embeddings of massive Yang-Mills theory
A power-counting renormalizable model into which massive Yang-Mills theory is
embedded is analyzed. The model is invariant under a nilpotent BRST
differential s. The physical observables of the embedding theory, defined by
the cohomology classes of s in the Faddeev-Popov neutral sector, are given by
local gauge-invariant quantities constructed only from the field strength and
its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the
journa
Geometric representation of interval exchange maps over algebraic number fields
We consider the restriction of interval exchange transformations to algebraic
number fields, which leads to maps on lattices. We characterize
renormalizability arithmetically, and study its relationships with a
geometrical quantity that we call the drift vector. We exhibit some examples of
renormalizable interval exchange maps with zero and non-zero drift vector, and
carry out some investigations of their properties. In particular, we look for
evidence of the finite decomposition property: each lattice is the union of
finitely many orbits.Comment: 34 pages, 8 postscript figure
Constructive algebraic renormalization of the abelian Higgs-Kibble model
We propose an algorithm, based on Algebraic Renormalization, that allows the
restoration of Slavnov-Taylor invariance at every order of perturbation
expansion for an anomaly-free BRS invariant gauge theory. The counterterms are
explicitly constructed in terms of a set of one-particle-irreducible Feynman
amplitudes evaluated at zero momentum (and derivatives of them). The approach
is here discussed in the case of the abelian Higgs-Kibble model, where the zero
momentum limit can be safely performed. The normalization conditions are
imposed by means of the Slavnov-Taylor invariants and are chosen in order to
simplify the calculation of the counterterms. In particular within this model
all counterterms involving BRS external sources (anti-fields) can be put to
zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page
Explicit Bosonization of the Massive Thirring Model in 3+1 Dimensions
We bosonize the Massive Thirring Model in 3+1D for small coupling constant
and arbitrary mass. The bosonized action is explicitly obtained both in terms
of a Kalb-Ramond tensor field as well as in terms of a dual vector field. An
exact bosonization formula for the current is derived. The small and large mass
limits of the bosonized theory are examined in both the direct and dual forms.
We finally obtain the exact bosonization of the free fermion with an arbitrary
mass.Comment: Latex, 7 page
The Lattice Schwinger Model: Confinement, Anomalies, Chiral Fermions and All That
In order to better understand what to expect from numerical CORE computations
for two-dimensional massless QED (the Schwinger model) we wish to obtain some
analytic control over the approach to the continuum limit for various choices
of fermion derivative. To this end we study the Hamiltonian formulation of the
lattice Schwinger model (i.e., the theory defined on the spatial lattice with
continuous time) in gauge. We begin with a discussion of the solution
of the Hamilton equations of motion in the continuum, we then parallel the
derivation of the continuum solution within the lattice framework for a range
of fermion derivatives. The equations of motion for the Fourier transform of
the lattice charge density operator show explicitly why it is a regulated
version of this operator which corresponds to the point-split operator of the
continuum theory and the sense in which the regulated lattice operator can be
treated as a Bose field. The same formulas explicitly exhibit operators whose
matrix elements measure the lack of approach to the continuum physics. We show
that both chirality violating Wilson-type and chirality preserving SLAC-type
derivatives correctly reproduce the continuum theory and show that there is a
clear connection between the strong and weak coupling limits of a theory based
upon a generalized SLAC-type derivative.Comment: 27 pages, 3 figures, revte
A Generalized Gauge Invariant Regularization of the Schwinger Model
The Schwinger model is studied with a new one - parameter class of gauge
invariant regularizations that generalizes the usual point - splitting or
Fujikawa schemes. The spectrum is found to be qualitatively unchanged, except
for a limiting value of the regularizing parameter, where free fermions appear
in the spectrum.Comment: 16 pages, SINP/TNP/93-1
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