190 research outputs found
Towards Noncommutative Linking Numbers Via the Seiberg-Witten Map
In the present work some geometric and topological implications of
noncommutative Wilson loops are explored via the Seiberg-Witten map. In the
abelian Chern-Simons theory on a three dimensional manifold, it is shown that
the effect of noncommutativity is the appearance of new knots at the
-th order of the Seiberg-Witten expansion. These knots are trivial homology
cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials.
Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of
the gauge field is shown to be written as an expansion of the linking number of
this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In
the process we explicitly compute the noncommutative 'Jones-Witten' invariants
up to first order in the noncommutative parameter. Finally in order to exhibit
a physical example, we apply these ideas explicitly to the Aharonov-Bohm
effect. It is explicitly displayed at first order in the noncommutative
parameter, we also show the relation to the noncommutative Landau levels.Comment: 19 pages, 1 figur
Non-Abelian Born-Infeld theory without the square root
A non-Abelian Born-Infeld theory is presented. The square root structure that
characterizes the Dirac-Born-Infeld (DBI) action does not appear. The procedure
is based on an Abelian theory proposed by Erwin Schr\"{o}dinger that, as he
showed, is equivalent to Born-Infeld theory. We briefly mention other possible
similar proposals. Our results could be of interest in connection with string
theory and possible extensions of well known physical results in the usual
Born-Infeld Abelian case.Comment: 9 pages, no figures, revtex
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