Papers by Luis Fernando Urrutia
Physical Review D, 1991
We consider a large class of Dirac oscillator-type couplings that exhibit a three-dimensional hid... more We consider a large class of Dirac oscillator-type couplings that exhibit a three-dimensional hidden supersymmetry. A subclass of exactly soluble cases is determined by using the Infeld and Hull procedure. We find that the corresponding spectra possess a high degree of unphysical degeneracy, similar to the Dirac oscillator case. This difficulty is overcome by proposing a further generalization of this
Physical Review D, 2002
A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a sys... more 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.
Physical Review D, 2005
We develop a detailed analysis of synchrotron radiation in the effective Lorentz invariance viola... more 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.
Journal of High Energy Physics, 2008
Using the parent Lagrangian approach we construct a dual formulation, in the sense originally pro... more 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.
Physical Review D, 2003
The construction of dual theories for linearized gravity in four dimensions is considered. Our ap... more 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.
Journal of Physics A-mathematical and General, 1994
Starting from the expression for the superdeterminant of (xI-M), where M is an arbitrary supermat... more Starting from the expression for the superdeterminant of (xI-M), where M is an arbitrary supermatrix, we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its characteristic equation. Depending upon the factorization properties of the basic polynomials whose ratio defines the above mentioned determinant we are able to construct polynomials of lower degree which are also shown to be annihilated by the supermatrix. Some particular cases and examples are considered.
Physical Review D, 1991
Consistent coupling of the gravitino field to a gravitational background with torsion. LF Urrutia... more Consistent coupling of the gravitino field to a gravitational background with torsion. LF Urrutia Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior, CU 04510 México, DF, Mexico and ...
A {\em complex} canonical transformation is found that takes the fourth order derivative Pais-Uhl... more A {\em complex} canonical transformation is found that takes the fourth order derivative Pais-Uhlenbeck oscillator into two independent harmonic oscillators thus showing that this model has energy bounded from below, unitary time-evolution and no negative norm states, or ghosts. Such transformation yields a positive definite inner product consistent with reality conditions in the Hilbert space. The method is illustrated by eliminating the negative norm states in a complex oscillator. Extensions to other higher order mechanical models and field theory are discussed.
Synchrotron radiation is analyzed in the classical effective Lorentz invariance violating model o... more 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.
Physical Review Letters, 2000
Massive spin-1͞2 fields are studied in the framework of loop quantum gravity by considering a sta... more Massive spin-1͞2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale L much greater than Planck length ᐉ P , a spin-1͞2 field in flat spacetime. The discrete structure of spacetime at ᐉ P yields corrections to the field propagation at scale L . Neutrino bursts (p ഠ 10 5 GeV) accompanying gamma ray bursts that have traveled cosmological distances L are considered. The dominant correction is helicity independent and leads to a time delay of order ͑pᐉ P ͒L͞c ഠ 10 4 s. To next order inpᐉ P , the correction has the form of the Gambini and Pullin effect for photons. A dependence L 21 os~p 2 ᐉ P is found for a two-flavor neutrino oscillation length. PACS numbers: 04.60.Ds, 14.60.Pq, 96.40.Tv, 98.70.Rz The fact that some gamma ray bursts (GRB) originate at cosmological distances (ഠ10 10 light years͒ [1], together with time resolutions down to submillisecond scale achieved in recent GRB data [2], suggests that it is possible to probe fundamental laws of physics at energy scales near to Planck energy E P 1.3 3 10 19 GeV . Furthermore, sensitivity will be improved with HEGRA and Whipple air Cherenkov telescopes and by AMS and GLAST spatial experiments. Thus, quantum gravity effects could be at the edge of observability . Now, quantum gravity theories imply different spacetime structures and it can be expected that what we consider flat spacetime can actually involve dispersive effects arising from Planck scale lengths. Such tiny effects might become observable upon accumulation over travels through cosmological distances by energetically enough particles like cosmological GRB photons.
General Relativity and Gravitation, 2007
We discuss a large class of phenomenological models incorporating quantum gravity motivated corre... more 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 Ω. The analysis of its effects upon the standard notion of causality is performed, showing that in the radiation regime (Ω R ≫ 1) the expected corrections of the order (ω/Ω)n get further suppressed by highly oscillating terms proportional to \(\sin(\Omega R), \cos(\Omega R)\) , thus forbiding causality violations to show up in the corresponding observational effects.
The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compact... more The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom has angular character. Not surprinsingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where $c$ takes values on the line. The main consequences are: the spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a $\theta$-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.
Physical Review D, 1995
Starting from an associated reparametrization-invariant action, the generalization of the BRST-BF... more Starting from an associated reparametrization-invariant action, the generalization of the BRST-BFV method for the case of nonstationary systems is constructed. The extension of the Batalin-Tyutin conversional approach is also considered in the nonstationary case. In order to illustrate these ideas, the propagator for the time-dependent two-dimensional rotor is calculated by reformulating the problem as a system with only first class constraints and subsequently using the BRST-BFV prescription previously obtained.
Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell ... more Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized in the manner of Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin and, for a value of a parameter of our approximation, that of Ellis and co-workers are recovered. The electric-magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological gamma ray bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.
General Relativity and Gravitation, 1999
Ashtekar canonical variables for generalrelativity yielding low degree polynomial constraintsare ... more Ashtekar canonical variables for generalrelativity yielding low degree polynomial constraintsare complex and describe complex canonical gravity. Topick the real sector, a la Dirac, one must introduce reality constraints; they turn out to besecond-class. It is shown here that this holds not onlyfor pure gravity but also for a scalar fieldnon-minimally coupled to gravity. The originalsimplicity produced by the complex variables is spoiled if one getsrid of the second-class constraints via Dirac brackets,however. To circumvent such an undesirable feature,alternative possibilities are pointed out.
Physical Review D, 2002
The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in ... more The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized a la Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological Gamma Ray Bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.
Physical Review D, 2002
Quantum gravity phenomenology opens up the possibility of probing Planck scale physics. Thus, by ... more Quantum gravity phenomenology opens up the possibility of probing Planck scale physics. Thus, by exploiting the generic properties that a semiclassical state of the compound system fermions plus gravity should have, an effective dynamics of spin-1/2 particles is obtained within the framework of loop quantum gravity. Namely, at length scales much larger than Planck length ᐉ P ϳ10 Ϫ33 cm and below the wavelength of the fermion, the spin-1/2 dynamics in flat spacetime includes Planck scale corrections. In particular we obtain modified dispersion relations in vacuo for fermions. These corrections yield a time of arrival delay of the spin-1/2 particles with respect to a light signal and, in the case of neutrinos, a novel flavor oscillation. To detect these effects the corresponding particles must be highly energetic and should travel long distances. Hence neutrino bursts accompanying gamma ray bursts or ultrahigh energy cosmic rays could be considered. Remarkably, future neutrino telescopes may be capable of testing such effects. This paper provides a detailed account of the calculations and elaborates on results previously reported in a Letter. These are further amended by introducing a real parameter ⌼ aimed at encoding our lack of knowledge of scaling properties of the gravitational degrees of freedom.
Physical Review D, 2004
Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassi... more Recent claims point out that possible violations of Lorentz symmetry appearing in some semiclassical models of extended matter dynamics motivated by loop quantum gravity can be removed by a different choice of canonically conjugated variables. In this note we show that such alternative is inconsistent with the choice of variables in the underlying quantum theory together with the semiclassical approximation, as long as the correspondence principle is maintained. A consistent choice will violate standard Lorentz invariance. Thus, to preserve a relativity principle in this framework, the linear realization of Lorentz symmetry should be extended or superseded.
A scalar field non-minimally coupled to gravity is studied in the canonical framework, using self... more A scalar field non-minimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes non-polynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the constraints, an alternative method preventing the use of Dirac brackets, is discussed. It consists of converting all second class constraints into first class by adding extra variables. This strategy is implemented for the pure gravity case.
Classical and Quantum Gravity, 1996
We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity c... more We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second class constraints.
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Papers by Luis Fernando Urrutia