2,513 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
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 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
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.
Regge calculus from a new angle
In Regge calculus space time is usually approximated by a triangulation with
flat simplices. We present a formulation using simplices with constant
sectional curvature adjusted to the presence of a cosmological constant. As we
will show such a formulation allows to replace the length variables by 3d or 4d
dihedral angles as basic variables. Moreover we will introduce a first order
formulation, which in contrast to using flat simplices, does not require any
constraints. These considerations could be useful for the construction of
quantum gravity models with a cosmological constant.Comment: 8 page
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
Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]
Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for
convergent series representations of both the real and the imaginary part of
the QED effective action; these derivations were based on correct intermediate
steps. In this comment, we argue that the physical significance of the
"logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86,
1947 (2001)] in comparison to the usual expression for the QED effective action
remains to be demonstrated. Further information on related subjects can be
found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update
Note About Hamiltonian Formalism of Healthy Extended Horava-Lifshitz Gravity
In this paper we continue the study of the Hamiltonian formalism of the
healthy extended Horava-Lifshitz gravity. We find the constraint structure of
given theory and argue that this is the theory with the second class
constraints. Then we discuss physical consequence of this result. We also apply
the Batalin-Tyutin formalism of the conversion of the system with the second
class constraints to the system with the first class constraints to the case of
the healthy extended Horava-Lifshitz theory. As a result we find new theory of
gravity with structure that is different from the standard formulation of
Horava-Lifshitz gravity or General Relativity.Comment: 17 pages, v.2. references added, v.3. typos corrected, references
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Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
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