R. Montemayor

Active sterile neutrino oscillations and pulsar kicks

Departamento de Fi ´sica de Altas Energias, Instituto de Ciencias Nucleares, Universidad Nacional Auto´nomadeMexico, Apartado Postal70-543, 04510 Me ´xico, Distrito Federal, Mexico~Received 24 February 2004; published 18 August 2004!We develop a thorough description of neutrino oscillations in a magnetized protoneutron star, based on aresonance layer for neutrinos with different momentum directions. We apply our approach to the calculation ofthe asymmetry in the neutrino emission during the birth of a neutron star and the pulsar acceleration in the caseof an active-sterile neutrino resonant conversion. The observed velocities can be obtained with the magneticfields expected in the interior of a protoneutron star, for sterile neutrino masses of the order of KeV and smallmixing angles.DOI: 10.1103/PhysRevD.70.043005 PACS number~s!: 97.60.Gb, 14.60.Pq, 98.70.RzI. INTRODUCTION

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

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

m

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

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 supernova remnants and gamma ray bursts.

Synchrotron radiation in Myers-Pospelov effective electrodynamics

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.

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

Abstract 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 ( μν ) ρ , which dynamically 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.

Duality for massive spin two theories in arbitrary dimensions

Abstract 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.

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

Abstract We analyze 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.

Duality for symmetric second rank tensors. 1. The Massive case

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 TA[B1B2...BD−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.

Reality and causality in quantum gravity modified electrodynamics

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{sub A[A{sub 1}A{sub 2}...A{sub D}{sub -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 inherit all the gauge symmetries of the original massless action and can be gauge fixed in two alternative ways, yielding the possibility of having a parent action with either a symmetric or a nonsymmetric Fierz-Pauli field e{sub AB}. Even though the dual sector in terms of the standard spin two field includes only the symmetrical part e{sub (AB)} in both cases, these two possibilities yield different results in terms of the alternative dual field T{sub A[A{sub 1}A{sub 2}...A{sub D}{sub -2}]}. In particular, the nonsymmetric case reproduces the Freund-Curtright action as the dual to the massive spin two field action in four dimensions.