10,086 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
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
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
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
International Legal Collections at U.S. Academic Law School Libraries
This study examines how law librarians are participating in the process of creating new fields of international legal research and training. It investigates the current state of international legal collections at twelve public and private U.S. academic law school libraries, illuminating in the process some of the significant shifts that characterize the nature of professional librarianship and information science in the twenty-first century. Included in the study is a discussion of the reference works, research guides, and databases that make up these international legal collections. This is followed by a brief assessment of the trends and challenges that librarians face who work in the field of professional legal education and scholarship
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