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 $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$, $\gamma$, and $\delta$ 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 δ\delta-δ′\delta^\prime 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 $q\to 0$ on a potential of the type $v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1} \delta'({y})$, when $u_0$ and $u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\mathbb R})$. 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 $v_1=\pm 1$, $w_1=\pm 1$ values of the $\delta^\prime$ couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side