25,574 research outputs found
Linear Form of Canonical Gravity
Recent work in the literature has shown that general relativity can be
formulated in terms of a jet bundle which, in local coordinates, has five
entries: local coordinates on Lorentzian space-time, tetrads, connection
one-forms, multivelocities corresponding to the tetrads and multivelocities
corresponding to the connection one-forms. The derivatives of the Lagrangian
with respect to the latter class of multivelocities give rise to a set of
multimomenta which naturally occur in the constraint equations. Interestingly,
all the constraint equations of general relativity are linear in terms of this
class of multimomenta. This construction has been then extended to complex
general relativity, where Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold. One then finds a
holomorphic theory where the familiar constraint equations are replaced by a
set of equations linear in the holomorphic multimomenta, providing such
multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum
gravity, the problem arises to quantize a real or a holomorphic theory on the
extended space where the multimomenta can be defined.Comment: 5 pages, plain-te
Tightening the uncertainty principle for stochastic currents
We connect two recent advances in the stochastic analysis of nonequilibrium
systems: the (loose) uncertainty principle for the currents, which states that
statistical errors are bounded by thermodynamic dissipation; and the analysis
of thermodynamic consistency of the currents in the light of symmetries.
Employing the large deviation techniques presented in [Gingrich et al., Phys.
Rev. Lett. 2016] and [Pietzonka et al., Phys. Rev. E 2016], we provide a short
proof of the loose uncertainty principle, and prove a tighter uncertainty
relation for a class of thermodynamically consistent currents . Our bound
involves a measure of partial entropy production, that we interpret as the
least amount of entropy that a system sustaining current can possibly
produce, at a given steady state. We provide a complete mathematical discussion
of quadratic bounds which allows to determine which are optimal, and finally we
argue that the relationship for the Fano factor of the entropy production rate
is the most significant
realization of the loose bound. We base our analysis both on the formalism of
diffusions, and of Markov jump processes in the light of Schnakenberg's cycle
analysis.Comment: 13 pages, 4 figure
Quantized Maxwell Theory in a Conformally Invariant Gauge
Maxwell theory can be studied in a gauge which is invariant under conformal
rescalings of the metric, and first proposed by Eastwood and Singer. This paper
studies the corresponding quantization in flat Euclidean 4-space. The resulting
ghost operator is a fourth-order elliptic operator, while the operator P on
perturbations of the potential is a sixth-order elliptic operator. The operator
P may be reduced to a second-order non-minimal operator if a dimensionless
gauge parameter tends to infinity. Gauge-invariant boundary conditions are
obtained by setting to zero at the boundary the whole set of perturbations of
the potential, jointly with ghost perturbations and their normal derivative.
This is made possible by the fourth-order nature of the ghost operator. An
analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost
basis functions has been amended, and the presentation has been improve
Essential self-adjointness in one-loop quantum cosmology
The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section
Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime
Recent work in the literature has studied rigid Casimir cavities in a weak
gravitational field, or in de Sitter spacetime, or yet other spacetime models.
The present review paper studies the difficult problem of direct evaluation of
scalar Green functions for a Casimir-type apparatus in de Sitter spacetime.
Working to first order in the small parameter of the problem, i.e. twice the
gravity acceleration times the plates' separation divided by the speed of light
in vacuum, suitable coordinates are considered for which the differential
equations obeyed by the zeroth- and first-order Green functions can be solved
in terms of special functions. This result can be used, in turn, to obtain, via
the point-split method, the regularized and renormalized energy-momentum tensor
both in the scalar case and in the physically more relevant electromagnetic
case.Comment: 13 pages, special issue review article. In the final version, the
calculations of Sec. III have been improved, two References have been added
and their content has been summarize
Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
We develop a consistent stochastic thermodynamics for environments composed
of thermodynamic reservoirs in an external conservative force field, that is
environments described by the Generalized or Gibbs canonical ensemble. We
demonstrate that small systems weakly coupled to such reservoirs exchange both
heat and work by verifying a local detailed balance relation for the induced
stochastic dynamics. Based on this analysis, we help to rationalize the
observation that nonthermal reservoirs can increase the efficiency of
thermodynamic heat engines.Comment: 6 pages, 1 figure, plus 3 page
Geometry and physics of pseudodifferential operators on manifolds
A review is made of the basic tools used in mathematics to define a calculus
for pseudodifferential operators on Riemannian manifolds endowed with a
connection: esistence theorem for the function that generalizes the phase;
analogue of Taylor's theorem; torsion and curvature terms in the symbolic
calculus; the two kinds of derivative acting on smooth sections of the
cotangent bundle of the Riemannian manifold; the concept of symbol as an
equivalence class. Physical motivations and applications are then outlined,
with emphasis on Green functions of quantum field theory and Parker's
evaluation of Hawking radiation.Comment: 14 pages, paper in honour of Gaetano Vilas
Hydrodynamic limit of asymmetric exclusion processes under diffusive scaling in
We consider the asymmetric exclusion process. We start from a profile which
is constant along the drift direction and prove that the density profile, under
a diffusive rescaling of time, converges to the solution of a parabolic
equation
Singularity Theory in Classical Cosmology
This paper compares recent approaches appearing in the literature on the
singularity problem for space-times with nonvanishing torsion.Comment: 4 pages, plain-tex, published in Nuovo Cimento B, volume 107, pages
849-851, year 199
Flavour-conserving oscillations of Dirac-Majorana neutrinos
We analyze both chirality-changing and chirality-preserving transitions of
Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect
to the others due to helicity conservation and the interactions with a
(``normal'') medium practically does not affect the expressions of the
probabilities for these transitions, even if the amplitudes of oscillations
slightly change. For usual situations involving relativistic neutrinos we find
no resonant enhancement for all flavour-conserving transitions. However, for
very light neutrinos propagating in superdense media, the pattern of
oscillations is dramatically altered with respect to the
vacuum case, the transition probability practically vanishing. An application
of this result is envisaged.Comment: 14 pages, latex 2E, no figure
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