1,454 research outputs found
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 ) the transformed
energy coincides with the standard one, both being . As the latter tends to
infinity under Lorentz transformations the former tends to a finite upper limit
where is the Planck length and the
mass-dependent nonleading terms vanish exactly for zero rest mass.The invariant
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 , 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 , 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 , the quantum gravity
effects show up in the opposite direction. However, these effects only manifest
themselves significantly when the temperature is larger than . 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 -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 (in addition to the speed-of-light scale ) is described
as an invariant. Just like the introduction of the invariant requires a
deformation of the Galileian transformations into the Lorentz transformations,
the introduction of the invariant 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
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