7,744 research outputs found
Complexified sigma model and duality
We show that the equations of motion associated with a complexified
sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process
we discover new type of numbers which we called `complexoids' in order to
emphasize their close relation with both complex numbers and matroids. It turns
out that the complexoids allow to consider the analogue of the complexified
sigma-model action but with (1+1)-worldsheet metric, instead of
Euclidean-worldsheet metric. Our observations can be useful for further
developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio
Canonical gravity in two time and two space dimensions
We describe a program for developing a canonical gravity in 2+2 dimensions
(two time and two space dimensions). Our procedure is similar to the usual
canonical gravity but with two times rather than just one time. Our work may be
of particular interest as an alternative approach to loop quantum gravity in
2+2 dimensions.Comment: 13 pages, Latex, improved versio
Linearized gravity as a gauge theory
We discuss linearized gravity from the point of view of a gauge theory. In
(3+1)-dimensions our analysis allows to consider linearized gravity in the
context of the MacDowell-Mansouri formalism. Our observations may be of
particular interest in the strong-weak coupling duality for linearized gravity,
in Randall-Sundrum brane world scenario and in Ashtekar formalism.Comment: Latex, 13 page
New hydrogen-like potentials
Using the modified factorization method introduced by Mielnik, we construct a
new class of radial potentials whose spectrum for l=0 coincides exactly with
that of the hydrogen atom. A limiting case of our family coincides with the
potentials previously derived by Abraham and MosesComment: 6 pages, latex, 2 Postscript figure
Equivalence between various versions of the self-dual action of the Ashtekar formalism
Different aspects of the self-dual (anti-self-dual) action of the Ashtekar
canonical formalism are discussed. In particular, we study the equivalences and
differences between the various versions of such an action. Our analysis may be
useful for the development of an Ashtekar formalism in eight dimensions.Comment: 10 pages, Latex, minor correction
Hamiltonian Noether theorem for gauge systems and two time physics
The Noether theorem for Hamiltonian constrained systems is revisited. In
particular, our review presents a novel method to show that the gauge
transformations are generated by the conserved quantities associated with the
first class constraints. We apply our results to the relativistic point
particle, to the Friedberg et al. model and, with special emphasis, to two time
physics.Comment: 20 pages, Latex, references added, the "massless" sense of (87) is
clarifie
Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri
Using MacDowell-Mansouri theory, in this work, we investigate a superfield
description of the self-dual supergravity a la Ashtekar. We find that in order
to reproduce previous results on supersymmetric Ashtekar formalism, it is
necessary to properly combine the supersymmetric field-strength in the
Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar
formalism in eight dimensions.Comment: 19 pages, Latex; section 6 improve
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