Galilean covariant Lagrangian models

We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Levy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.

Vortices in nonlocal Gross-Pitaevskii equation

We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to the polar angle, the unstable modes of the axial n-fold vortex have orbital numbers l satisfying 0 < \l\ < 2\n\, as in the local model. Numerical simulations show that nonlocality slightly decreases the threshold rotation frequency above which the nonvortex state ceases to be the global energy minimum and decreases the frequency of the anomalous mode of the 1-vortex. In the case of higher axial vortices, nonlocality leads to instability against splitting with the creation of antivortices and gives rise to additional anomalous modes with higher orbital numbers. Despite new instability channels with the creation of antivortices, for a stationary solution comprised of vortices and antivortices there always exists another vortex solution, composed solely of vortices, with the same total vorticity but with a lower energy.

On the worldsheet derivation of large N dualities for the superstring

Large N topological string dualities have led to a class of proposed open/ closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a (c) over cap = 5 topological string in ten-dimensional spacetime. Using the (c) over cap = 5 description, we then show that the D brane boundary state for the ten-dimensional open superstring naturally emerges on the worldsheet of the closed superstring dual.

Teleparallel equivalent of non-Abelian Kaluza-Klein theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

Exact Foldy-Wouthuysen transformation for real spin-0 particle in curved space

Up to now, the only known exact Foldy-Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one-third of the corresponding term in the fermionic case. There are some arguments in the literature that seem to favor the choice lambda=1/6. We rehearse a number of claims of these works.

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity-associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime-we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal 'radial' d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this 'radial' equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.

Pion interactions in the X(3872)

We consider pion interactions in an effective field theory of the narrow resonance X(3872), assuming it is a weakly bound molecule of the charm mesons D-0(D) over bar (*0) and D-*0(D) over bar (0). Since the hyperfine splitting of the D-0 and D-*0 is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are nonrelativistic. We show that pion exchange can be treated in perturbation theory and calculate the next-to-leading-order correction to the partial decay width Gamma[X -> D-0(D) over bar (0)pi(0)].

Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this held theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We examine the recently found equivalence for the response of a static scalar source interacting with a massless Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation, and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a massive one.

Semiclassical approach to black hole absorption of electromagnetic radiation emitted by a rotating charge

We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness of the results obtained in a full general relativistic approach in comparison with the ones obtained when the electric charge is assumed to be orbiting a massive object due to a Newtonian force.

A dynamical mechanism to explain the top-bottom quark mass hierarchy

We discuss the mass splitting between the the top and bottom quarks in a technicolor scenario. The model proposed here contains a left-right electroweak gauge group. An extended technicolor group and mirror fermions are introduced. The top-bottom quark mass splitting turns out to be intimately connected to the breaking of the left-right gauge symmetry. Weak isospin violation occurs within the experimental limits.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

Quantization of the superstring in Ramond-Ramond backgrounds

Sigma model actions are constructed for the type II superstring compactified to four-and six-dimensional curved backgrounds which can contain non-vanishing Ramond-Ramond fields. These actions are N = 2 worldsheet superconformally invariant and can be covariantly quantized preserving manifest spacetime supersymmetry. They are constructed using a hybrid Version of superstring variables which combines features of the Ramond-Neveu-Schwarz and Green-Schwarz formalisms. For the AdS(2) x S-2 and AdS(3) x S-3 backgrounds, these actions differ from the classical Green-Schwarz actions by a crucial kinetic term for the fermions. Parts of this work have been done in collaborations with M Bershadsky, T Hauer, W Siegel, C Vafa, E Witten, S Zhukov and B Zwiebach.

Teleparallel origin of the Fierz picture for spin-2 particle

A new approach to the description of a spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz representation proposed recently by Novello and Neves. More specifically, we demonstrate how the teleparallel theory fixes uniquely the structure of the Fierz tensor, discover the transparent origin of the gauge symmetry of the spin-2 model, and derive the linearized Einstein operator from the fundamental identity of the teleparallel gravity. In order to cope with the consistency problem on the curved spacetime, similarly to the usual Riemannian approach, one needs to include the nonminimal (torsion dependent) coupling terms.

Cosmological term and fundamental physics

A nonvanishing cosmological term in Einstein's equations implies a nonvanishing spacetime curvature even in the absence of any kind of matter. It would, in consequence, affect many of the underlying kinematic tenets of physical theory. The usual commutative spacetime translations of the Poincare group would be replaced by the mixed conformal translations of the de Sitter group, leading to obvious alterations in elementary concepts such as time, energy and momentum. Although negligible at small scales, such modifications may come to have important consequences both in the large and for the inflationary picture of the early Universe. A qualitative discussion is presented, which suggests deep changes in Hamiltonian, Quantum and Statistical Mechanics. In the primeval universe as described by the standard cosmological model, in particular, the equations of state of the matter sources could be quite different from those usually introduced.