235 research outputs found
Bicomplexes, Integrable Models, and Noncommutative Geometry
We discuss a relation between bicomplexes and integrable models, and consider
corresponding noncommutative (Moyal) deformations. As an example, a
noncommutative version of a Toda field theory is presented.Comment: 6 pages, 1 figure, LaTeX using amssymb.sty and diagrams.sty, to
appear in Proceedings of the 1999 Euroconference "Noncommutative geometry and
Hopf algebras in Field Theory and Particle Physics
Black branes in four-dimensional conformal equivalent theories
The physical properties of static analytic solutions which describe black
brane geometries are discussed. In particular we study the similarities and
differences of analytic black brane/string solutions in the Einstein and Jordan
frames. The comparison is made between vacuum power law gravity
solutions and their conformal equivalents in the Einstein frame. In our
analysis we examine how the geometrical and physical properties of these
analytic axisymmetric solutions - such as singularities, the temperature and
the entropy - are affected as we pass from one frame to the other.Comment: 12 pages, no figure
Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions
We study static and transport properties of Skyrmions living within a finite
spatial volume in a flat (3+1)-dimensional spacetime. In particular, we derive
an explicit analytic expression for the compression modulus corresponding to
these Skyrmions living within a finite box and we show that such expression can
produce a reasonable value. The gauged version of these solitons can be also
considered. It is possible to analyze the order of magnitude of the
contributions to the electrons conductivity associated to the interactions with
this Baryonic environment. The typical order of magnitude for these
contributions\ to conductivity can be compared with the experimental values of
the conductivity of layers of Baryons.Comment: Latex2e source file, 30 pages, 7 figures, accepted for publication in
European Physical Journal
Differential Calculi on Commutative Algebras
A differential calculus on an associative algebra A is an algebraic analogue
of the calculus of differential forms on a smooth manifold. It supplies A with
a structure on which dynamics and field theory can be formulated to some extent
in very much the same way we are used to from the geometrical arena underlying
classical physical theories and models. In previous work, certain differential
calculi on a commutative algebra exhibited relations with lattice structures,
stochastics, and parametrized quantum theories. This motivated the present
systematic investigation of differential calculi on commutative and associative
algebras. Various results about their structure are obtained. In particular, it
is shown that there is a correspondence between first order differential
calculi on such an algebra and commutative and associative products in the
space of 1-forms. An example of such a product is provided by the Ito calculus
of stochastic differentials.
For the case where the algebra A is freely generated by `coordinates' x^i,
i=1,...,n, we study calculi for which the differentials dx^i constitute a basis
of the space of 1-forms (as a left A-module). These may be regarded as
`deformations' of the ordinary differential calculus on R^n. For n < 4 a
classification of all (orbits under the general linear group of) such calculi
with `constant structure functions' is presented. We analyse whether these
calculi are reducible (i.e., a skew tensor product of lower-dimensional
calculi) or whether they are the extension (as defined in this article) of a
one dimension lower calculus. Furthermore, generalizations to arbitrary n are
obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose
tiling was incorrect in the first version of the paper (p. 14
Bicomplexes and Integrable Models
We associate bicomplexes with several integrable models in such a way that
conserved currents are obtained by a simple iterative construction. Gauge
transformations and dressings are discussed in this framework and several
examples are presented, including the nonlinear Schrodinger and sine-Gordon
equations, and some discrete models.Comment: 17 pages, LaTeX, uses amssymb.sty and diagrams.st
(Compactified) black branes in four dimensional f(R)-gravity
A new family of analytical solutions in a four dimensional static spacetime
is presented for -gravity. In contrast to General
Relativity, we find that a non trivial black string/ring solution is supported
in vacuum power law -gravity for appropriate values of the
parameters characterizing the model and when axisymmetry is introduced in the
line element. For the aforementioned solution, we perform a brief investigation
over its basic thermodynamic quantities.Comment: 13 pages, 3 figures, title changed, minor corrections, new
references, accepted version for publication at Physics Letter
A new approach to deformation equations of noncommutative KP hierarchies
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP)
hierarchy, we start with a quite general hierarchy of linear ordinary
differential equations in a space of matrices and derive from it a matrix
Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly
nonassociative' (WNA) algebra structure, from which we can conclude, refering
to previous work, that any solution of the Riccati system also solves the
potential KP hierarchy (in the corresponding matrix algebra). We then turn to
the case where the components of the matrices are multiplied using a
(generalized) star product. Associated with the deformation parameters, there
are additional symmetries (flow equations) which enlarge the respective KP
hierarchy. They have a compact formulation in terms of the WNA structure. We
also present a formulation of the KP hierarchy equations themselves as
deformation flow equations.Comment: 25 page
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