30 research outputs found
Statistical Thermodynamics of Polymer Quantum Systems
Polymer quantum systems are mechanical models quantized similarly as loop
quantum gravity. It is actually in quantizing gravity that the polymer term
holds proper as the quantum geometry excitations yield a reminiscent of a
polymer material. In such an approach both non-singular cosmological models and
a microscopic basis for the entropy of some black holes have arisen. Also
important physical questions for these systems involve thermodynamics. With
this motivation, in this work, we study the statistical thermodynamics of two
one dimensional {\em polymer} quantum systems: an ensemble of oscillators that
describe a solid and a bunch of non-interacting particles in a box, which thus
form an ideal gas. We first study the spectra of these polymer systems. It
turns out useful for the analysis to consider the length scale required by the
quantization and which we shall refer to as polymer length. The dynamics of the
polymer oscillator can be given the form of that for the standard quantum
pendulum. Depending on the dominance of the polymer length we can distinguish
two regimes: vibrational and rotational. The first occur for small polymer
length and here the standard oscillator in Schr\"odinger quantization is
recovered at leading order. The second one, for large polymer length, features
dominant polymer effects. In the case of the polymer particles in the box, a
bounded and oscillating spectrum that presents a band structure and a Brillouin
zone is found. The thermodynamical quantities calculated with these spectra
have corrections with respect to standard ones and they depend on the polymer
length. For generic polymer length, thermodynamics of both systems present an
anomalous peak in their heat capacity
On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance
A simple model is constructed which allows to compute modified dispersion
relations with effects from loop quantum gravity. Different quantization
choices can be realized and their effects on the order of corrections studied
explicitly. A comparison with more involved semiclassical techniques shows that
there is agreement even at a quantitative level.
Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show
that possible Lorentz symmetry violations may be blurred as an artifact of the
approximation scheme. Whether this is the case in a purely Hamiltonian analysis
can be resolved by an improvement in the effective semiclassical analysis.Comment: 16 pages, RevTeX
Quantum gravity corrections to neutrino propagation
Massive spin-1/2 fields are studied in the framework of loop quantum gravity
by considering a state approximating, at a length scale much greater
than Planck length cm, a spin-1/2 field in flat
spacetime. The discrete structure of spacetime at yields corrections
to the field propagation at scale . Next, Neutrino Bursts (GeV) accompaning Gamma Ray Bursts that have travelled
cosmological distances, l.y., are considered. The dominant
correction is helicity independent and leads to a time delay w.r.t. the speed
of light, , of order s. To next order in
the correction has the form of the Gambini and Pullin effect
for photons. Its contribution to time delay is comparable to that caused by the
mass term. Finally, a dependence is
found for a two-flavour neutrino oscillation length.Comment: RevTeX, 5pp, no figures. Notation of a sum in Eq.(2) improved. Slight
modifications in redaction. Final version to appear in Phys. Rev. Let
Casimir force for a scalar field in warped brane worlds
In looking for imprints of extra dimensions in brane world models one usually
builts these so that they are compatible with known low energy physics and thus
focuses on high energy effects. Nevertheless, just as submillimeter Newton's
law tests probe the mode structure of gravity other low energy tests might
apply to matter. As a model example, in this work we determine the 4D Casimir
force corresponding to a scalar field subject to Dirichlet boundary conditions
on two parallel planes lying within the single brane of a Randall-Sundrum
scenario extended by one compact extra dimension. Using the Green's function
method such a force picks the contribution of each field mode as if it acted
individually but with a weight given by the square of the mode wave functions
on the brane. In the low energy regime one regains the standard 4D Casimir
force that is associated to a zero mode in the massless case or to a
quasilocalized or resonant mode in the massive one whilst the effect of the
extra dimensions gets encoded as an additional term.Comment: 22 pages, 2 figure
Reality conditions for Ashtekar variables as Dirac constraints
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.Comment: 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail:
[email protected]
Self-Dual Action for Fermionic Fields and Gravitation
This paper studies the self-dual Einstein-Dirac theory. A generalization is
obtained of the Jacobson-Smolin proof of the equivalence between the self-dual
and Palatini purely gravitational actions. Hence one proves equivalence of
self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac
theory. The Bianchi symmetry of the curvature, core of the proof, now contains
a non-vanishing torsion. Thus, in the self-dual framework, the extra terms
entering the equations of motion with respect to the standard Einstein-Dirac
field equations, are neatly associated with torsion.Comment: 13 pages, plain-tex, recently appearing in Nuovo Cimento B, volume
109, pages 973-982, September 199