13,836 research outputs found
Quantum Gravity and Inflation
Using the Ashtekar-Sen variables of loop quantum gravity, a new class of
exact solutions to the equations of quantum cosmology is found for gravity
coupled to a scalar field, that corresponds to inflating universes. The scalar
field, which has an arbitrary potential, is treated as a time variable,
reducing the hamiltonian constraint to a time-dependent Schroedinger equation.
When reduced to the homogeneous and isotropic case, this is solved exactly by a
set of solutions that extend the Kodama state, taking into account the time
dependence of the vacuum energy. Each quantum state corresponds to a classical
solution of the Hamiltonian-Jacobi equation. The study of the latter shows
evidence for an attractor, suggesting a universality in the phenomena of
inflation. Finally, wavepackets can be constructed by superposing solutions
with different ratios of kinetic to potential scalar field energy, resolving,
at least in this case, the issue of normalizability of the Kodama state.Comment: 18 Pages, 2 Figures; major corrections to equations but prior results
still hold, updated reference
An Arena for Model Building in the Cohen-Glashow Very Special Relativity
The Cohen-Glashow Very Special Relativity (VSR) algebra
[arXiv:hep-ph/0601236] is defined as the part of the Lorentz algebra which upon
addition of CP or T invariance enhances to the full Lorentz group, plus the
space-time translations. We show that noncommutative space-time, in particular
noncommutative Moyal plane, with light-like noncommutativity provides a robust
mathematical setting for quantum field theories which are VSR invariant and
hence set the stage for building VSR invariant particle physics models. In our
setting the VSR invariant theories are specified with a single deformation
parameter, the noncommutativity scale \Lambda_{NC}. Preliminary analysis with
the available data leads to \Lambda_{NC}\gtrsim 1-10 TeV.
This note is prepared for the Proceedings of the G27 Mathematical Physics
Conference, Yerevan 2008, and is based on arXiv:0806.3699[hep-th].Comment: Presented by M.M.Sh-J. in the G27 Mathematical Physics Conference,
Yerevan 2008 as the 4th Weyl Prize Ceremony Tal
Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations
The technique of continuous unitary transformations has recently been used to
provide physical insight into a diverse array of quantum mechanical systems.
However, the question of how to best numerically implement the flow equations
has received little attention. The most immediately apparent approach, using
standard Runge-Kutta numerical integration algorithms, suffers from both severe
inefficiency due to stiffness and the loss of unitarity. After reviewing the
formalism of continuous unitary transformations and Wegner's original choice
for the infinitesimal generator of the flow, we present a number of approaches
to resolving these issues including a choice of generator which induces what we
call the "uniform tangent decay flow" and three numerical integrators
specifically designed to perform continuous unitary transformations efficiently
while preserving the unitarity of flow. We conclude by applying one of the flow
algorithms to a simple calculation that visually demonstrates the many-body
localization transition.Comment: 13 pages, 4 figures, Comments welcom
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