Consistency analysis of a nonbirefringent Lorentz-violating planar model

In this work analyze the physical consistency of a nonbirefringent Lorentz-violating planar model via the analysis of the pole structure of its Feynman propagators. The nonbirefringent planar model, obtained from the dimensional reduction of the CPT-even gauge sector of the standard model extension, is composed of a gauge and a scalar fields, being affected by Lorentz-violating (LIV) coefficients encoded in the symmetric tensor $\kappa_{\mu\nu}$. The propagator of the gauge field is explicitly evaluated and expressed in terms of linear independent symmetric tensors, presenting only one physical mode. The same holds for the scalar propagator. A consistency analysis is performed based on the poles of the propagators. The isotropic parity-even sector is stable, causal and unitary mode for $0\leq\kappa_{00}<1$. On the other hand, the anisotropic sector is stable and unitary but in general noncausal. Finally, it is shown that this planar model interacting with a $\lambda|\varphi|^{4}-$Higgs field supports compactlike vortex configurations.Comment: 11 pages, revtex style, final revised versio

SO(2,1) conformal anomaly: Beyond contact interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio

Algebraic Structures and Eigenstates for Integrable Collective Field Theories

Conditions for the construction of polynomial eigen--operators for the Hamiltonian of collective string field theories are explored. Such eigen--operators arise for only one monomial potential $v(x) = \mu x^2$ in the collective field theory. They form a $w_{\infty}$--algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non--zero--energy polynomial eigen--operators. This analysis leads us to consider a particular potential $v(x)= \mu x^2 + g/x^2$. A Lie algebra of polynomial eigen--operators is then constructed for this potential. It is a symmetric 2--index Lie algebra, also represented as a sub--algebra of $U (s\ell (2)).$Comment: 27 page

Threshold analyses and Lorentz violation

In the context of threshold investigations of Lorentz violation, we discuss the fundamental principle of coordinate invariance, the role of an effective dynamical framework, and the conditions of positivity and causality. Our analysis excludes a variety of previously considered Lorentz-breaking parameters and opens an avenue for viable dispersion-relation investigations of Lorentz violation.Comment: 9 page

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the Harmonic Oscillator

In this work, we obtain bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present a new possible scenario of studying the Lorentz symmetry breaking effects on a nonrelativistic quantum system defined by a fixed space-like vector field parallel to the radial direction interacting with a uniform magnetic field along the z-axis. Furthermore, we also discuss the influence of a Coulomb-like potential induced by Lorentz symmetry violation effects on the two-dimensional harmonic oscillator.Comment: 14 pages, no figure, this work has been accepted for publication in The European Physical Journal Plu

Dark Matter and Fundamental Physics with the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is a project for a next-generation observatory for very high energy (GeV-TeV) ground-based gamma-ray astronomy, currently in its design phase, and foreseen to be operative a few years from now. Several tens of telescopes of 2-3 different sizes, distributed over a large area, will allow for a sensitivity about a factor 10 better than current instruments such as H.E.S.S, MAGIC and VERITAS, an energy coverage from a few tens of GeV to several tens of TeV, and a field of view of up to 10 deg. In the following study, we investigate the prospects for CTA to study several science questions that influence our current knowledge of fundamental physics. Based on conservative assumptions for the performance of the different CTA telescope configurations, we employ a Monte Carlo based approach to evaluate the prospects for detection. First, we discuss CTA prospects for cold dark matter searches, following different observational strategies: in dwarf satellite galaxies of the Milky Way, in the region close to the Galactic Centre, and in clusters of galaxies. The possible search for spatial signatures, facilitated by the larger field of view of CTA, is also discussed. Next we consider searches for axion-like particles which, besides being possible candidates for dark matter may also explain the unexpectedly low absorption by extragalactic background light of gamma rays from very distant blazars. Simulated light-curves of flaring sources are also used to determine the sensitivity to violations of Lorentz Invariance by detection of the possible delay between the arrival times of photons at different energies. Finally, we mention searches for other exotic physics with CTA.Comment: (31 pages, Accepted for publication in Astroparticle Physics

Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope

We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing the delay between gamma-rays of different energies as \Delta t =\pm\tau_l E or \Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigma level, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use these results to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} > 0.26x10^{11} GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC sensitivity to propagation effects at these levels. Thermal plasma effects in the source are negligible, but we cannot exclude the importance of some other source effect.Comment: 12 pages, 3 figures, Phys. Lett. B, reflects published versio