3,356 research outputs found
Reduced Phase Space Quantization and Dirac Observables
In her recent work, Dittrich generalized Rovelli's idea of partial
observables to construct Dirac observables for constrained systems to the
general case of an arbitrary first class constraint algebra with structure
functions rather than structure constants. Here we use this framework and
propose a new way for how to implement explicitly a reduced phase space
quantization of a given system, at least in principle, without the need to
compute the gauge equivalence classes. The degree of practicality of this
programme depends on the choice of the partial observables involved. The
(multi-fingered) time evolution was shown to correspond to an automorphism on
the set of Dirac observables so generated and interesting representations of
the latter will be those for which a suitable preferred subgroup is realized
unitarily. We sketch how such a programme might look like for General
Relativity. We also observe that the ideas by Dittrich can be used in order to
generate constraints equivalent to those of the Hamiltonian constraints for
General Relativity such that they are spatially diffeomorphism invariant. This
has the important consequence that one can now quantize the new Hamiltonian
constraints on the partially reduced Hilbert space of spatially diffeomorphism
invariant states, just as for the recently proposed Master constraint
programme.Comment: 18 pages, no figure
A perturbative approach to Dirac observables and their space-time algebra
We introduce a general approximation scheme in order to calculate gauge
invariant observables in the canonical formulation of general relativity. Using
this scheme we will show how the observables and the dynamics of field theories
on a fixed background or equivalently the observables of the linearized theory
can be understood as an approximation to the observables in full general
relativity. Gauge invariant corrections can be calculated up to an arbitrary
high order and we will explicitly calculate the first non--trivial correction.
Furthermore we will make a first investigation into the Poisson algebra between
observables corresponding to fields at different space--time points and
consider the locality properties of the observables.Comment: 23 page
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
We develop a gauge invariant canonical perturbation scheme for perturbations
around symmetry reduced sectors in generally covariant theories, such as
general relativity. The central objects of investigation are gauge invariant
observables which encode the dynamics of the system. We apply this scheme to
perturbations around a homogeneous and isotropic sector (cosmology) of general
relativity. The background variables of this homogeneous and isotropic sector
are treated fully dynamically which allows us to approximate the observables to
arbitrary high order in a self--consistent and fully gauge invariant manner.
Methods to compute these observables are given. The question of backreaction
effects of inhomogeneities onto a homogeneous and isotropic background can be
addressed in this framework. We illustrate the latter by considering
homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a
homogeneous and isotropic sector.Comment: 39 pages, 1 figur
Improved and Perfect Actions in Discrete Gravity
We consider the notion of improved and perfect actions within Regge calculus.
These actions are constructed in such a way that they - although being defined
on a triangulation - reproduce the continuum dynamics exactly, and therefore
capture the gauge symmetries of General Relativity. We construct the perfect
action in three dimensions with cosmological constant, and in four dimensions
for one simplex. We conclude with a discussion about Regge Calculus with curved
simplices, which arises naturally in this context.Comment: 28 pages, 2 figure
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
In our companion paper we identified a complete set of manifestly
gauge-invariant observables for general relativity. This was possible by
coupling the system of gravity and matter to pressureless dust which plays the
role of a dynamically coupled observer. The evolution of those observables is
governed by a physical Hamiltonian and we derived the corresponding equations
of motion. Linear perturbation theory of those equations of motion around a
general exact solution in terms of manifestly gauge invariant perturbations was
then developed. In this paper we specialise our previous results to an FRW
background which is also a solution of our modified equations of motion. We
then compare the resulting equations with those derived in standard
cosmological perturbation theory (SCPT). We exhibit the precise relation
between our manifestly gauge-invariant perturbations and the linearly
gauge-invariant variables in SCPT. We find that our equations of motion can be
cast into SCPT form plus corrections. These corrections are the trace that the
dust leaves on the system in terms of a conserved energy momentum current
density. It turns out that these corrections decay, in fact, in the late
universe they are negligible whatever the value of the conserved current. We
conclude that the addition of dust which serves as a test observer medium,
while implying modifications of Einstein's equations without dust, leads to
acceptable agreement with known results, while having the advantage that one
now talks about manifestly gauge-invariant, that is measurable, quantities,
which can be used even in perturbation theory at higher orders.Comment: 51 pages, no figure
Simplicity in simplicial phase space
A key point in the spin foam approach to quantum gravity is the
implementation of simplicity constraints in the partition functions of the
models. Here, we discuss the imposition of these constraints in a phase space
setting corresponding to simplicial geometries. On the one hand, this could
serve as a starting point for a derivation of spin foam models by canonical
quantisation. On the other, it elucidates the interpretation of the boundary
Hilbert space that arises in spin foam models.
More precisely, we discuss different versions of the simplicity constraints,
namely gauge-variant and gauge-invariant versions. In the gauge-variant
version, the primary and secondary simplicity constraints take a similar form
to the reality conditions known already in the context of (complex) Ashtekar
variables. Subsequently, we describe the effect of these primary and secondary
simplicity constraints on gauge-invariant variables. This allows us to
illustrate their equivalence to the so-called diagonal, cross and edge
simplicity constraints, which are the gauge-invariant versions of the
simplicity constraints. In particular, we clarify how the so-called gluing
conditions arise from the secondary simplicity constraints. Finally, we discuss
the significance of degenerate configurations, and the ramifications of our
work in a broader setting.Comment: Typos and references correcte
Neutrino self-energy in a magnetized medium in arbitrary -gauge
We calculate the one-loop neutrino self-energy in a magnetized plasma to all
orders in the magnetic field. The calculation is done in a general gauge. We
obtain the dispersion relation and effective potential for neutrinos in a
CP-symmetric plasma under various conditions, and show that, while the
self-energy depends on the gauge parameter , the dispersion relation and
effective potential to leading order are independent of it.Comment: 13 pages, RevTeX, epsfig, axodra
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