973 research outputs found
An Efficient Method for the Solution of Schwinger--Dyson equations for propagators
Efficient computation methods are devised for the perturbative solution of
Schwinger--Dyson equations for propagators. We show how a simple computation
allows to obtain the dominant contribution in the sum of many parts of previous
computations. This allows for an easy study of the asymptotic behavior of the
perturbative series. In the cases of the four-dimensional supersymmetric
Wess--Zumino model and the complex scalar field, the singularities
of the Borel transform for both positive and negative values of the parameter
are obtained and compared.Comment: 9 pages, no figures. Match of the published version, with the
corrections in proo
Singularity, complexity, and quasi--integrability of rational mappings
We investigate global properties of the mappings entering the description of
symmetries of integrable spin and vertex models, by exploiting their nature of
birational transformations of projective spaces. We give an algorithmic
analysis of the structure of invariants of such mappings. We discuss some
characteristic conditions for their (quasi)--integrability, and in particular
its links with their singularities (in the 2--plane). Finally, we describe some
of their properties {\it qua\/} dynamical systems, making contact with
Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM
On the Symmetries of Integrability
We show that the Yang-Baxter equations for two dimensional models admit as a
group of symmetry the infinite discrete group . The existence of
this symmetry explains the presence of a spectral parameter in the solutions of
the equations. We show that similarly, for three-dimensional vertex models and
the associated tetrahedron equations, there also exists an infinite discrete
group of symmetry. Although generalizing naturally the previous one, it is a
much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to
resolve the Yang-Baxter equations and their higher-dimensional generalizations
and initiate the study of three-dimensional vertex models. These symmetries are
naturally represented as birational projective transformations. They may
preserve non trivial algebraic varieties, and lead to proper parametrizations
of the models, be they integrable or not. We mention the relation existing
between spin models and the Bose-Messner algebras of algebraic combinatorics.
Our results also yield the generalization of the condition so often
mentioned in the theory of quantum groups, when no parameter is available.Comment: 23 page
Singularity confinement and algebraic integrability
Two important notions of integrability for discrete mappings are algebraic
integrability and singularity confinement, have been used for discrete
mappings. Algebraic integrability is related to the existence of sufficiently
many conserved quantities whereas singularity confinement is associated with
the local analysis of singularities. In this paper, the relationship between
these two notions is explored for birational autonomous mappings. Two types of
results are obtained: first, algebraically integrable mappings are shown to
have the singularity confinement property. Second, a proof of the non-existence
of algebraic conserved quantities of discrete systems based on the lack of
confinement property is given.Comment: 18 pages, no figur
New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: Classical and Quantal Analysis
Recently proposed new gauge invariant formulation of the Chern-Simons gauge
theory is considered in detail. This formulation is consistent with the gauge
fixed formulation. Furthermore it is found that the canonical (Noether)
Poincar\'e generators are not gauge invariant even on the constraints surface
and do not satisfy the Poincar\'e algebra contrast to usual case. It is the
improved generators, constructed from the symmetric energy-momentum tensor,
which are (manifestly) gauge invariant and obey the quantum as well as
classical Poincar\'e algebra. The physical states are constructed and it is
found in the Schr\"odinger picture that unusual gauge invariant longitudinal
mode of the gauge field is crucial for constructing the physical wavefunctional
which is genuine to (pure) Chern-Simons theory. In matching to the gauge fixed
formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges
as explicit examples. Furthermore, recent several confusions about the effect
of Dirac's dressing function and the gauge fixings are clarified. The analysis
according to old gauge independent formulation a' la Dirac is summarized in an
appendix.Comment: No figures, 44 page
Symmetrical Temperature-Chaos Effect with Positive and Negative Temperature Shifts in a Spin Glass
The aging in a Heisenberg-like spin glass Ag(11 at% Mn) is investigated by
measurements of the zero field cooled magnetic relaxation at a constant
temperature after small temperature shifts . A
crossover from fully accumulative to non-accumulative aging is observed, and by
converting time scales to length scales using the logarithmic growth law of the
droplet model, we find a quantitative evidence that positive and negative
temperature shifts cause an equivalent restart of aging (rejuvenation) in terms
of dynamical length scales. This result supports the existence of a unique
overlap length between a pair of equilibrium states in the spin glass system.Comment: 4 page
Baxterization, dynamical systems, and the symmetries of integrability
We resolve the `baxterization' problem with the help of the automorphism
group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations.
This infinite group of symmetries is realized as a non-linear (birational)
Coxeter group acting on matrices, and exists as such, {\em beyond the narrow
context of strict integrability}. It yields among other things an unexpected
elliptic parametrization of the non-integrable sixteen-vertex model. It
provides us with a class of discrete dynamical systems, and we address some
related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are
BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to
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