38 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
Brane world corrections to scalar vacuum force in RSII-p
Vacuum force is an interesting low energy test for brane worlds due to its
dependence on field's modes and its role in submillimeter gravity experiments.
In this work we generalize a previous model example: the scalar field vacuum
force between two parallel plates lying in the brane of a Randall-Sundrum
scenario extended by compact dimensions (RSII-). Upon use of Green's
function technique, for the massless scalar field, the 4D force is obtained
from a zero mode while corrections turn out attractive and depend on the
separation between plates as . For the massive scalar field a
quasilocalized mode yields the 4D force with attractive corrections behaving
like . Corrections are negligible w.r.t. 4D force for
radius less than m. Although the case is not
physically viable due to the different behavior in regard to localization for
the massless scalar and electromagnetic fields it yields an useful comparison
between the dimensional regularization and Green's function techniques as we
describe in the discussion.Comment: 14 pages, v2: discussion clarified, reference adde
Loop Variables for compact two-dimensional quantum electrodynamics
Variables parametrized by closed and open curves are defined to reformulate
compact U(1) Quantum Electrodynamics in the circle with a massless fermion
field. It is found that the gauge invariant nature of these variables
accommodates into a regularization scheme for the Hamiltonian and current
operators that is specially well suited for the study of the compact case. The
zero mode energy spectrum, the value of the axial anomaly and the anomalous
commutators this model presents are hence determined in a manifestly gauge
invariant manner. Contrary to the non compact case, the zero mode spectrum is
not equally spaced and consequently the theory does not lead to the spectrum of
a free scalar boson. All the states are invariant under large gauge
transformations. In particular, that is the case for the vacuum, and
consequently the -dependence does not appear.Comment: 24 pages, 1 figure, to be published in Phys. Rev.
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