3,340 research outputs found
(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
Tunneling And The Onset Of Chaos In A Driven Bistable System
We study the interplay between coherent transport by tunneling and diffusive
transport through classically chaotic phase-space regions, as it is reflected
in the Floquet spectrum of the periodically driven quartic double well. The
tunnel splittings in the semiclassical regime are determined with high
numerical accuracy, and the association of the corresponding doublet states to
either chaotic or regular regions of the classical phase space is quantified in
terms of the overlap of the Husimi distribution with the chaotic layer along
the separatrix. We find a strong correlation between both quantities. They show
an increase by orders of magnitude as chaotic diffusion between the wells
starts to dominate the classical dynamics. We discuss semiclassical
explanations for this correlation.Comment: 17 pages in REVTeX preprint format. A version with encapsulated
Postscript figures included (via epsf) and GIF-images of wave functions are
available from the Gopher server aix.rz.uni-augsburg (port 300) in directory
U Augsburg/Inst.f.Physik/Lst.f.Theo.PhysI/Tunneling an
Spin foam models with finite groups
Spin foam models, loop quantum gravity and group field theory are discussed
as quantum gravity candidate theories and usually involve a continuous Lie
group. We advocate here to consider quantum gravity inspired models with finite
groups, firstly as a test bed for the full theory and secondly as a class of
new lattice theories possibly featuring an analogue diffeomorphism symmetry. To
make these notes accessible to readers outside the quantum gravity community we
provide an introduction to some essential concepts in the loop quantum gravity,
spin foam and group field theory approach and point out the many connections to
lattice field theory and condensed matter systems.Comment: 47 pages, 6 figure
Curved planar quantum wires with Dirichlet and Neumann boundary conditions
We investigate the discrete spectrum of the Hamiltonian describing a quantum
particle living in the two-dimensional curved strip. We impose the Dirichlet
and Neumann boundary conditions on opposite sides of the strip. The existence
of the discrete eigenvalue below the essential spectrum threshold depends on
the sign of the total bending angle for the asymptotically straight strips.Comment: 7 page
From covariant to canonical formulations of discrete gravity
Starting from an action for discretized gravity we derive a canonical
formalism that exactly reproduces the dynamics and (broken) symmetries of the
covariant formalism. For linearized Regge calculus on a flat background --
which exhibits exact gauge symmetries -- we derive local and first class
constraints for arbitrary triangulated Cauchy surfaces. These constraints have
a clear geometric interpretation and are a first step towards obtaining
anomaly--free constraint algebras for canonical lattice gravity. Taking higher
order dynamics into account the symmetries of the action are broken. This
results in consistency conditions on the background gauge parameters arising
from the lowest non--linear equations of motion. In the canonical framework the
constraints to quadratic order turn out to depend on the background gauge
parameters and are therefore pseudo constraints. These considerations are
important for connecting path integral and canonical quantizations of gravity,
in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version +
updated references
QED effective action at finite temperature
The QED effective Lagrangian in the presence of an arbitrary constant
electromagnetic background field at finite temperature is derived in the
imaginary-time formalism to one-loop order. The boundary conditions in
imaginary time reduce the set of gauge transformations of the background field,
which allows for a further gauge invariant and puts restrictions on the choice
of gauge. The additional invariant enters the effective action by a topological
mechanism and can be identified with a chemical potential; it is furthermore
related to Debye screening. In concordance with the real-time formalism, we do
not find a thermal correction to Schwinger's pair-production formula. The
calculation is performed on a maximally Lorentz covariant and gauge invariant
stage.Comment: 9 pages, REVTeX, 1 figure, typos corrected, references added, final
version to appear in Phys. Rev.
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
Classical GR as a topological theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained topological (BF) theory, in the spirit of the Plebanski
formulation, but involving only linear constraints, of the type used recently
in the spin foam approach to quantum gravity. We identify both the continuum
version of the linear simplicity constraints used in the quantum discrete
context and a linear version of the quadratic volume constraints that are
necessary to complete the reduction from the topological theory to gravity. We
illustrate and discuss also the discrete counterpart of the same continuum
linear constraints. Moreover, we show under which additional conditions the
discrete volume constraints follow from the simplicity constraints, thus
playing the role of secondary constraints. Our analysis clarifies how the
discrete constructions of spin foam models are related to a continuum theory
with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010
(ERE2010, Granada, Spain
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