9,553 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
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
Functional Forms for the Squeeze and the Time-Displacement Operators
Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator
time-displacement operators are given in the form , where ,
, , and are explicitly determined. Applications are
discussed.Comment: 10 pages, LaTe
Propagation of localized surface plasmons in sets of metallic nanocylinders at the exit of subwavelength slits
We analyze, by means of numerical simulations, transmission enhancements
through sub- wavelength slits due to the presence of sets of plasmonic
nanocylinders, placed near the exit of these apertures. Further, we extend this
study to photonic crystals of dipolar plasmonic particles in front of an array
of extraordinarily transmitting slits practiced in a metallic slab.Comment: 20 pages, 9 figures. Submitted to Journal of Nanophotonic
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
Two-point one-dimensional - interactions: non-abelian addition law and decoupling limit
In this contribution to the study of one dimensional point potentials, we
prove that if we take the limit on a potential of the type
, we
obtain a new point potential of the type , when and are related to , , and
by a law having the structure of a group. This is the Borel subgroup of
. We also obtain the non-abelian addition law from the
scattering data. The spectra of the Hamiltonian in the exceptional cases
emerging in the study are also described in full detail. It is shown that for
the , values of the couplings the
singular Kurasov matrices become equivalent to Dirichlet at one side of the
point interaction and Robin boundary conditions at the other side
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