117,876 research outputs found
Chern-Simons Field Theory and Completely Integrable Systems
We show that the classical non-abelian pure Chern-Simons action is related in
a natural way to completely integrable systems of the Davey-Stewartson
hyerarchy, via reductions of the gauge connection in Hermitian spaces and by
performing certain gauge choices. The B\"acklund Transformations are
interpreted in terms of Chern-Simons equations of motion or, on the other hand,
as a consistency condition on the gauge. A mapping with a nonlinear
-model is discussed.Comment: 11 pages, Late
Dynamics in the magnetic/dual magnetic monopole
Inspired by the geometrical methods allowing the introduction of mechanical
systems confined in the plane and endowed with exotic galilean symmetry, we
resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide
class of 3D systems, involving not commuting and/or not canonical variables,
but possessing geometric as well gauge symmetries in position and momenta space
too. As a paradigmatic example, a charged particle simultaneously interacting
with a magnetic monopole and a dual monopole in momenta space is considered.
The main features of the motions, conservation laws and the analogies with the
planar case are discussed. Possible physical realizations of the model are
proposed.Comment: 15 pages, 1 figure, based on a talk for the QTS7 conference, Prague,
August 7-13 (2011), accepted in Journal of Physics: Conference Serie
A looping-delooping adjunction for topological spaces
Every principal G-bundle is classified up to equivalence by a homotopy class
of maps into the classifying space of G. On the other hand, for every nice
topological space Milnor constructed a strict model of loop space, that is a
group. Moreover the morphisms of topological groups defined on the loop space
of X generate all the bundles over X up to equivalence. In this paper, we show
that the relationship between Milnor's loop space and the classifying space
functor is, in a precise sense, an adjoint pair between based spaces and
topological groups in a homotopical context. This proof leads to a
classification of principal bundles with a fixed structure group. Such a resul
clarifies the deep relation that exists between the theory of bundles, the
classifying space construction and the loop space construction, which are very
important in topological K-theory, group cohomology and homotopy theory.Comment: v1: 24 pages; v2: 18 pages; Corrected typos; Revised structure in
Introduction, and Sections 1 and 2; Results unchange
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