J. L. Cortes

Quantum uncertainty in doubly special relativity

A discussion of the modification of the phase-space commutators in a quantum mechanical relativistic theory with an invariant length scale (DSR) is presented. Two examples are discussed where a classical behavior is approached in one case when the energy approaches the inverse of the invariant length which appears as a cutoff in the energy and in the second case when the mass is much larger than the inverse of the invariant length.

ANYONS AS SPINNING PARTICLES

A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are investigated. The relationship between all the known approaches to anyons as spinning particles is established. Some widespread misleading notions on the general properties of (2+1)-dimensional anyons are removed.

Super-extended noncommutative Landau problem and conformal symmetry

A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an arbitrary magnetic field, is considered, with particular attention paid to the homogeneous case. The system has three different phases, depending on the magnetic field. Due to supersymmetry, the boundary critical phase which separates the sub- and super-critical cases can be viewed as a reduction to the zero-energy eigensubspace. In the sub-critical phase the system is described by the superextension of exotic Newton-Hooke symmetry, combined with the conformal so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the super-critical phase. In the critical phase the spin degrees of freedom are frozen and supersymmetry disappears.

Linear differential equations for a fractional spin field

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite‐dimensional half‐bounded unitary representations of the SL(2,R) group. In the case of (2j+1)‐dimensional nonunitary representations of that group, 0<2j∈Z, they are transformed into equations for spin‐j fields. A local gauge symmetry associated to the vector system of equations is identified and the simplest gauge invariant field action, leading to these equations, is constructed.

Testing Lorentz invariance violations in the tritium beta decay anomaly

We consider a Lorentz non-invariant dispersion relation for the neutrino, which would produce unexpected effects with neutrinos of few eV, exactly where the tritium beta-decay anomaly is found. We use this anomaly to put bounds on the violation of Lorentz invariance. We discuss other consequences of this non-invariant dispersion relation in neutrino experiments and high-energy cosmic-ray physics.

A pseudoclassical model for the massive Dirac particle in d dimensions

Abstract A new pseudoclassical model is proposed for the description of the relativistic massive Dirac particle. It is P - and T -noninvariant in the case of odd space-time dimensions. The quantization of the model leads exactly to the corresponding d -dimensional Dirac equation for arbitrary d , conserving its P - and T -noninvariance at the quantum level for the case of odd d .

Particle and antiparticle sectors in DSR1 and κ-Minkowski space-time

In this paper we explore the problem of antiparticles in DSR1 and κ-Minkowski space-time following three different approaches inspired by the Lorentz invariant case: (a) the dispersion relation, (b) the Dirac equation in space-time and (c) the Dirac equation in momentum space. We find that it is possible to define a map Sdsr which gives the antiparticle sector from the negative frequency solutions of the wave equation. In κ-Poincare, the corresponding map Skp is the antipodal mapping, which is different from Sdsr. The difference is related to the composition law, which is crucial to define the multiparticle sector of the theory. This discussion permits to show that the energy of the antiparticle in DSR is the positive root of the dispersion relation, which is consistent with phenomenological approaches.

MATTER–ANTIMATTER ASYMMETRY GENERATED AT LOW TEMPERATURES

We explore the possibility of baryogenesis without departure from thermal equilibrium. A possible scenario is found, though it contains strong constraints on the size of the

Effective field theory of gravity, reduction of couplings, and the renormalization group.

CPT

Locality and the relativity principle beyond special relativity

violation (