arXiv subjects

R. Montemayor

Publications and source records attributed to R. Montemayor.

At least 19 recordsLinked to original sources

arXiv2013

A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity

After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach. For the one particle case, the starting point is a de Sitter momentum space in five dimensions, with an additional constraint selected to recover the mass shell condition in four dimensions. Different basis of DSR can be recovered by selecting specific gauges to define the reduced four dimensional degrees of freedom. This is shown for the Snyder basis in the one particle case. We generalize the method to the many particles case and apply it again to this basis. We show that the energy and momentum of the system, given by the dynamical variables that are generators of translations in space and time and which close the Poincaré algebra, are additive magnitudes. From this it results that the rest energy (mass) of a composite object does not have an upper limit, as opposed to a single component particle which does.

hep-th↗

arXiv2012

Emergent electrodynamics from the Nambu model for spontaneous Lorentz symmetry breaking

After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_μA^μ=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the spontaneously broken symmetry, which finally turns out to be non-observable

hep-th↗

arXiv2011

Perturbative Hamiltonian constraints for higher order theories

We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory. This comparison highligths the soundness of the present formalism.

hep-th↗

arXiv2008

Dimensional reduction as a method to obtain dual theories for massive spin two in arbitray dimensions

Using the parent Lagrangian method together with a dimensional reduction from $D$ to $(D-1)$ dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor $T_{A[A_{1}A_{2}... A_{D-2}]}$. Our starting point is the well studied massless parent action in dimension $D$. The resulting massive Stueckelberg-like parent actions in $(D-1)$ dimensions inherits all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having either a parent action with a symmetric or a non-symmetric Fierz-Pauli field $e_{AB}$. Even though the dual sector in terms of the standard spin two field includes only the symmetrical part $e_{\{AB\}}$ in both cases, these two possibilities yield different results in terms of the alternative dual field $T_{A[A_{1}A_{2}... A_{D-2}]}$. In particular, the non-symmetric case reproduces the Freund-Curtright action as the dual to the massive spin two field action in four dimensions.

hep-th↗

arXiv2008

Duality for massive spin two theories in arbitrary dimensions

Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a Fierz-Pauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.

hep-th↗

arXiv2007

Phenomenological description of quantum gravity inspired modified classical electrodynamics

We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive relations, which are considered up to second order in the inverse of the energy characterizing the quantum gravity scale. The energy-momentum tensor, Green functions and frequency dependent refraction indices are obtained, leading to departures from standard physics. The effective character of the theory is also emphasized by introducing a frequency cutoff. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime the expected corrections get further suppressed by highly oscillating terms, thus forbiding causality violations to show up in the corresponding observational effects.

gr-qc↗

arXiv2006

Reality and causality in quantum gravity modified electrodynamics

We present a general description of the propagation properties of quantum gravity modified electrodynamics characterized by constitutive relations up to second order in the correction parameter. The effective description corresponds to an electrodynamics in a dispersive and absorptive non-local medium, where the Green functions and the refraction indices can be explicitly calculated. The reality of the electromagnetic field together with the requirement of causal propagation in a given referrence frame leads to restrictions in the form of such refraction indices. In particular, absorption must be present in all cases and, contrary to the usual assumption, it is the dominant aspect in those effective models which exhibit linear effects in the correction parameter not related to birefringence. In such a situation absorption is linear while propagation is quadratical in the correction parameter.

gr-qc↗

arXiv2005

Synchrotron Radiation in Lorentz-violating Electrodynamics: the Myers-Pospelov model

We develop a detailed analysis of synchrotron radiation in the effective Lorentz invariance violating (LIV) model of Myers-Pospelov, considering explicitly both the dynamics of the charge producing the radiation and the dynamics of the electromagnetic field itself. Within the radiation approximation we compute exact expressions in the LIV parameters for the electric and magnetic fields, the angular distribution of the power spectrum, the total emitted power in the m-th harmonic and the polarization. We also perform expansions of the exact results in terms of the LIV parameters to identify the dominant effects, and study the main features of the high energy limit of the spectrum. A very interesting consequence is the appearance of rather unexpected and large amplifying factors associated with the LIV effects, which go along with the usual contributions of the expansion parameter. This opens up the possibility of looking for astrophysical sources where these amplifying factors are important to further explore the constraints imposed upon the LIV parameters by synchrotron radiation measurements. We briefly sketch some phenomenological applications in the case of SNRs and GRBs.

hep-ph↗

arXiv2005

Lorentz violating electrodynamics

After summarizing the most interesting results in the calculation of synchrotron radiation in the Myers-Pospelov effective model for Lorentz invariance violating (LIV) electrodynamics, we present a general unified way of describing the radiation regime of LIV electrodynamics which include the following three different models : Gambini-Pullin, Ellis et al. and Myers-Pospelov. Such unification reduces to the standard approach of radiation in a dispersive and absortive (in general) medium with a given index of refraction. The formulation is presented up to second order in the LIV parameter and it is explicitly applied to the synchrotron radiation case.

hep-ph↗

arXiv2005

Neutrinospheres, resonant neutrino oscillations, and pulsar kicks

Pulsars are rapidly rotating neutron stars and are the outcome of the collapse of the core of a massive star with a mass of the order of or larger than eight solar masses. This process releases a huge gravitational energy of about 10^{53} erg, mainly in the form of neutrinos. During the collapse the density increases, and so does the magnetic field due to the trapping of the flux lines of the progenitor star by the high conductivity plasma. When the density reaches a value of around 10^{12} g cm^{-3} neutrinos become trapped within the protoneutron star and a neutrinosphere, characterized inside by a diffusive transport of neutrinos and outside by a free streaming of neutrinos, is formed and lasts for a few seconds. Here we focus on the structure of the neutrinosphere, the resonant flavor conversion that can happen in its interior, and the neutrino flux anisotropies induced by this phenomena in the presence of a strong magnetic field. We present a detailed discussion in the context of the spherical Eddington model, which provides a simple but reasonable description of a static neutrino atmosphere, locally homogenous and isotropic. Energy and momentum are transported by neutrinos and antineutrinos flowing through an ideal gas of nonrelativistic, nondegenerate nucleons and relativistic, degenerate electrons and positrons. We examine the details of the asymmetric neutrino emission driven by active-sterile neutrino oscillations in the magnetized protoneutron star, and the possibility for this mechanism to explain the intrinsic large velocities of pulsars respect to nearby stars and associated supernova remnants.

hep-ph↗

arXiv2004

Radiation in Lorentz violating electrodynamics

Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model of Myers-Pospelov. Within the full far-field approximation we compute the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic, as well as the polarization. We find the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of further exploring Lorentz invariance violations by synchrotron radiation measurements in astrophysical sources where these amplifying factors are important.

hep-ph↗

arXiv2004

Synchrotron radiation in Myers-Pospelov effective electrodynamics

In the framework of the classical effective Lorentz invariance violating (LIV) model of Myers-Pospelov, we present a complete calculation of the synchrotron radiation produced by a circularly moving charge in the rest frame of the model. Within the full far-field approximation we compute exact expressions for the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the m-th harmonic. We also perform an expansion of the latter quantity in terms of the electromagnetic LIV parameter and calculate the average degree of circular polarization to first order in such a parameter. In both cases we find, under adequate circumstances, the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of selecting astrophysical sources where these amplifying factors are important, to explore further constraints imposed upon the LIV parameters by synchrotron radiation measurements.

hep-ph↗

arXiv2004

Active-sterile neutrino oscillations and pulsar kicks

We develop a thorough description of neutrino oscillations in a magnetized protoneutron star, based on a resonance layer for neutrinos with different momentum directions. We apply our approach to the calculation of the asymmetry in the neutrino emission during the birth of a neutron star and the pulsar acceleration in the case of an active-sterile neutrino resonant conversion. The observed velocities can be obtained with the magnetic fields expected in the interior of a protoneutron star, for sterile neutrino masses of the order of KeV and small mixing angles.

hep-ph↗

arXiv2003

Duality for symmetric second rank tensors. II. The linearized gravitational field

The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples illustrating the general procedure and the physical interpretation of the dual fields. The zero mass case of the massive theory dual to the massive spin-two theory is also examined, but we show that it only contains a spin-zero excitation.

hep-th↗

arXiv2002

Neutrino oscillation mechanism for pulsar kicks reexamined

Anisotropic neutrino emission during the neutron star formation can be the origin of the observed proper motions of pulsars. We derive a general expression for the momentum asymmetry in terms of the neutrino energy flux gradient, and show that a nonvanishing effect is induced at the lowest order by a deformed neutrinosphere. In particular, this result is valid for a neutrino flux transported through a spherical atmosphere with constant luminosity.

astro-ph↗

arXiv2002

Duality for symmetric second rank tensors.(I): the massive case

A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a systematic scheme for constructing the dual descriptions is developed. The method, a purely Lagrangian approach, is based on a first order parent Lagrangian, from which the dual partners are generated. In particular, a family of theories which are dual to the massive spin two Fierz-Pauli field, both free and coupled to an external source, is constructed in terms of a third rank tensor which is taken as the basic configuration variable.

hep-th↗

arXiv2001

Dual theories for mixed symmetry fields. Spin-two case: (1,1) versus (2,1) Young symmetry type fields

We show that the parent Lagrangian method gives a natural generalization of the dual theories concept for non p-form fields. Using this generalization we construct here a three-parameter family of Lagrangians that are dual to the Fierz-Pauli description of a free massive spin-two system. The dual field is a three-index tensor T, which dinamically belongs to the (2,1) representation of the Lorentz group. As expected, the massless limit of our Lagrangian, which is parameter independent, has two propagating degrees of freedom per space point.

hep-th↗

arXiv2001

Pulsar motions from neutrino oscillations induced by a violation of the equivalence principle

We analize a possible explanation of the pulsar motions in terms of resonant neutrino transitions induced by a violation of the equivalence principle (VEP). Our approach, based on a parametrized post-Newtonian (PPN) expansion, shows that VEP effects give rise to highly directional contributions to the neutrino oscillation length. These terms induce anisotropies in the linear and angular momentum of the emitted neutrinos, which can account for both the observed translational and rotational pulsar motions. The violation needed to produce the actual motions is completely compatible with the existing bounds.

astro-ph↗