Nonlinear transforms of momenta and Planck scale limit

Starting with the generators of the Poincar\'e group for arbitrary mass (m) and spin (s) a nonunitary transformation is implemented to obtain momenta with an absolute Planck scale limit. In the rest frame (for $m>0$) the transformed energy coincides with the standard one, both being $m$. As the latter tends to infinity under Lorentz transformations the former tends to a finite upper limit $m\coth(lm) = l^{-1}+ O(l)$ where $l$ is the Planck length and the mass-dependent nonleading terms vanish exactly for zero rest mass.The invariant $m^{2}$ is conserved for the transformed momenta. The speed of light continues to be the absolute scale for velocities. We study various aspects of the kinematics in which two absolute scales have been introduced in this specific fashion. Precession of polarization and transformed position operators are among them. A deformation of the Poincar\'e algebra to the SO(4,1) deSitter one permits the implementation of our transformation in the latter case. A supersymmetric extension of the Poincar\'e algebra is also studied in this context.Comment: 10 pages, no figures, corrected some typo

Deformed dispersion relations and the degree of coherence function

The analysis of the modifications that the presence of a deformed dispersion relation entails in the roots of the so--called degree of coherence function, for a beam embodying two different frequencies and moving in a Michelson interferometer, is carried out. The conditions to be satisfied, in order to detect this kind of quantum gravity effect, are also obtained

Photon Gas Thermodynamics in Doubly Special Relativity

Doubly special relativity (DSR), with both an invariant velocity and an invariant length scale, elegantly preserves the principle of relativity between moving observers, and appears as a promising candidate of the quantum theory of gravity. We study the modifications of photon gas thermodynamics in the framework of DSR with an invariant length $|\lambda|$, after properly taking into account the effects of modified dispersion relation, upper bounded energy-momentum space, and deformed integration measure. We show that with a positive $\lambda$, the grand partition function, the energy density, the specific heat, the entropy, and the pressure are smaller than those of special relativity (SR), while the velocity of photons and the ratio of pressure to energy are larger. In contrast, with a negative $\lambda$, the quantum gravity effects show up in the opposite direction. However, these effects only manifest themselves significantly when the temperature is larger than $10^{-3} E_{\rm P}$. Thus, DSR can have considerable influence on the early universe in cosmological study.Comment: 17 pages, 7 figures, final version for publication in AP

Cosmic rays and TeV photons as probes of quantum properties of space-time

It has been recently observed that small violations of Lorentz invariance, of a type which may arise in quantum gravity, could explain both the observations of cosmic rays above the GZK cutoff and the observations of 20-TeV gamma rays from Markarian 501. We show here that different pictures of the short-distance structure of space-time would lead to different manifestations of Lorentz-invariance violation. Specifically, the deformation of Lorentz invariance needed to resolve these observational paradoxes can only arise within commutative short-distance pictures of space-time. In noncommutative space-times there is no anomalous effect, at least at leading order. Also exploiting the fact that arrival-time delays between high energy photons with different energies would arise in both the commutative and the noncommutative Lorentz-violation pictures, we describe an experimental programme, based on time-of-arrival analysis of high energy photons and searches of violations of GZK and TeV-photon limits, which could discriminate between alternative scenarios of Lorentz-invariance breakdown and could provide and unexpected window on the (quantum) nature of space-time at very short distances.Comment: 8 pages, LaTe

Space-time quantum solves three experimental paradoxes

I show that a Planck-scale deformation of the relativistic dispersion relation, which has been independently considered in the quantum-gravity literature, can explain the surprising results of three classes of experiments: (1) observations of cosmic rays above the expected GZK limit, (2) observations of multi-TeV photons from the BL Lac object Markarian 501, (3) studies of the longitudinal development of the air showers produced by ultra-high-energy hadronic particles. Experiments now in preparation, such as the ones planned for the GLAST space telescope, will provide an independent test of this solution of the three experimental paradoxes.Comment: LaTex, 9 pages. Typos corrected (in the version submitted yesterday there was one type in equation and a couple of spelling typos). All aspects of the analysis remain unchange

Group of boost and rotation transformations with two observer-independent scales

I examine the structure of the deformed Lorentz transformations in one of the recently-proposed schemes with two observer-independent scales. I develop a technique for the analysis of general combinations of rotations and deformed boosts. In particular, I verify explicitly that the transformations form group.Comment: revised version accepted for publication on Phys.Lett.B; one reference corrected, some physical comments added. 6 pages, RevTex

Deformed Boost Transformations That Saturate at the Planck Scale

We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of these boost transformations in a recently-proposed new relativistic theory. We find that when the (dimensionful) deformation parameter is identified with the Planck length, which together with the speed-of-light constant has the status of observer-independent scale in the new relativistic theory, the deformed boosts saturate at the value of momentum that corresponds to the inverse of the Planck length.Comment: 6 pages, LaTex (revtex

Kinematical solution of the UHE-cosmic-ray puzzle without a preferred class of inertial observers

Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakup of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale $E_p$ (in addition to the speed-of-light scale $c$) is described as an invariant. Just like the introduction of the invariant $c$ requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant $E_p$ requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides being the first one to provide a solution for the cosmic-ray puzzle, is also the first one in which a natural description of macroscopic bodies is achieved, and may find applications in the context of a recently-proposed dark-energy scenario.Comment: LaTex (revtex), 9 page

Calogero-Sutherland Particles as Quasisemions

The ultraviolet structure of the Calogero-Sutherland models is examined, and, in particular, semions result to have special properties. An analogy with ultraviolet structures known in anyon quantum mechanics is drawn, and it is used to suggest possible physical consequences of the observed semionic properties.Comment: 7 pages, LaTe