2,093 research outputs found
Non-renormalization theorems without supergraphs: The Wess-Zumino model
The non-renormalization theorems of chiral vertex functions are derived on
the basis of an algebraic analysis. The property, that the interaction vertex
is a second supersymmetry variation of a lower dimensional field monomial, is
used to relate chiral Green functions to superficially convergent Green
functions by extracting the two supersymmetry variations from an internal
vertex and transforming them to derivatives acting on external legs. The
analysis is valid in the massive as well as in the massless model and can be
performed irrespective of properties of the superpotential at vanishing
momentum.Comment: 20 pages, Latex, added acknowledgment
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
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
Massless Decoupled Doublers: Chiral Yukawa Models and Chiral Gauge Theories
We present a new method for regularizing chiral theories on the lattice. The
arbitrariness in the regularization is used in order to decouple massless
replica fermions. A continuum limit with only one fermion is obtained in
perturbation theory and a Golterman-Petcher like symmetry related to the
decoupling of the replicas in the non-perturbative regime is identified. In the
case of Chiral Gauge Theories gauge invariance is broken at the level of the
regularization, so our approach shares many of the characteristics of the Rome
approach.Comment: 11 page
Higher-order non-symmetric counterterms in pure Yang-Mills theory
We analyze the restoration of the Slavnov-Taylor (ST) identities for pure
massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization
scheme with IR regulator. We obtain the most general form of the action-like
part of the symmetric regularized action, obeying the relevant ST identities
and all other relevant symmetries of the model, to all orders in the loop
expansion. We also give a cohomological characterization of the fulfillment of
BPHZL IR power-counting criterion, guaranteeing the existence of the limit
where the IR regulator goes to zero. The technique analyzed in this paper is
needed in the study of the restoration of the ST identities for those models,
like the MSSM, where massless particles are present and no invariant
regularization scheme is known to preserve the full set of ST identities of the
theory.Comment: Final version published in the journa
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
Hyperbolic outer billiards : a first example
We present the first example of a hyperbolic outer billiard. More precisely
we construct a one parameter family of examples which in some sense correspond
to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit
On the trace identity in a model with broken symmetry
Considering the simple chiral fermion meson model when the chiral symmetry is
explicitly broken, we show the validity of a trace identity -- to all orders of
perturbation theory -- playing the role of a Callan-Symanzik equation and which
allows us to identify directly the breaking of dilatations with the trace of
the energy-momentum tensor. More precisely, by coupling the quantum field
theory considered to a classical curved space background, represented by the
non-propagating external vielbein field, we can express the conservation of the
energy-momentum tensor through the Ward identity which characterizes the
invariance of the theory under the diffeomorphisms. Our ``Callan-Symanzik
equation'' then is the anomalous Ward identity for the trace of the
energy-momentum tensor, the so-called ``trace identity''.Comment: 11 pages, Revtex file, final version to appear in Phys.Rev.
Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime
Using the monomer--dimer representation of the lattice Schwinger model, with
Wilson fermions in the strong--coupling regime (), we
evaluate its partition function, , exactly on finite lattices. By studying
the zeroes of in the complex plane for a large number of
small lattices, we find the zeroes closest to the real axis for infinite
stripes in temporal direction and spatial extent and 3. We find evidence
for the existence of a critical value for the hopping parameter in the
thermodynamic limit on the real axis at about . By looking at the behaviour of quantities, such as the chiral
condensate, the chiral susceptibility and the third derivative of with
respect to , close to the critical point , we find some indications
for a continuous phase transition.Comment: 22 pages (6 figures
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