343 research outputs found
Generalised group field theories and quantum gravity transition amplitudes
We construct a generalised formalism for group field theories, in which the
domain of the field is extended to include additional proper time variables, as
well as their conjugate mass variables. This formalism allows for different
types of quantum gravity transition amplitudes in perturbative expansion, and
we show how both causal spin foam models and the usual a-causal ones can be
derived from it, within a sum over triangulations of all topologies. We also
highlight the relation of the so-derived causal transition amplitudes with
simplicial gravity actions.Comment: RevTeX; 6 pages, 2 figure
Dynamics of relativistic particle with Lagrangian dependent on acceleration
Models of relativistic particle with Lagrangian , depending on
the curvature of the worldline , are considered. By making use of the
Frenet basis, the equations of motion are reformulated in terms of the
principal curvatures of the worldline. It is shown that for arbitrary
Lagrangian function these equations are completely integrable,
i.e., the principal curvatures are defined by integrals. The constants of
integration are the particle mass and its spin. The developed method is applied
to the study of a model of relativistic particle with maximal proper
acceleration, whose Lagrangian is uniquely determined by a modified form of the
invariant relativistic interval. This model gives us an example of a consistent
relativistic dynamics obeying the principle of a superiorly limited value of
the acceleration, advanced recently.Comment: 15 pages, LATEX, Preprint Salerno University DFT-US-3/9
Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry
A lower bound on the light neutrino mass is derived in the framework
of a geometrical interpretation of quantum mechanics. Using this model and the
time of flight delay data for neutrinos coming from SN1987A, we find that the
neutrino masses are bounded from below by eV, in
agreement with the upper bound
eV currently available. When the model is applied to photons with effective
mass, we obtain a lower limit on the electron density in intergalactic space
that is compatible with recent baryon density measurements.Comment: 22 pages, 3 figure
Neutrinos in a vacuum dominated cosmology
We explore the dynamics of neutrinos in a vacuum dominated cosmology. First
we show that such a geometry will induce a phase change in the eigenstates of a
massive neutrino and we calculate the phase change. We also calculate the delay
in the neutrino flight times in this geometry. Applying our results to the
presently observed background vacuum energy density, we find that for neutrino
sources further than away both effects become non-trivial, being of
the order of the standard relativistic corrections. Such sources are within the
obsevable Hubble Deep Field. The results which are theoretically interesting
are also potentially useful, in the future, as detection techniques improve.
For example such effects on neutrinos from distant sources like supernovae
could be used, in an independent method alternative to standard candles, to
constrain the dark energy density and the deceleration parameter. The
discussion is extended to investigate Caianiello's inertial or maximal
acceleration (MA) effects of such a vacuum dominated spacetime on neutrino
oscillations. Assuming that the MA phenomenon exists, we find that its form as
generated by the presently observed vacuum energy density would still have
little or no measurable effect on neutrino phase evolution.Comment: 10 pages, LaTeX, no figure
Optical measurements of phase steps in segmented mirrors - fundamental precision limits
Phase steps are an important type of wavefront aberrations generated by large
telescopes with segmented mirrors. In a closed-loop correction cycle these
phase steps have to be measured with the highest possible precision using
natural reference stars, that is with a small number of photons. In this paper
the classical Fisher information of statistics is used for calculating the
Cramer-Rao bound, which determines the limit to the precision with which the
height of the steps can be estimated in an unbiased fashion with a given number
of photons and a given measuring device. Four types of measurement devices are
discussed: a Shack-Hartmann sensor with one small cylindrical lenslet covering
a sub-aperture centred over a border, a modified Mach-Zehnder interferometer, a
Foucault test, and a curvature sensor. The Cramer-Rao bound is calculated for
all sensors under ideal conditions, that is narrowband measurements without
additional noise or disturbances apart from the photon shot noise. This limit
is compared with the ultimate quantum statistical limit for the estimate of
such a step which is independent of the measuring device. For the
Shack-Hartmann sensor, the effects on the Cramer-Rao bound of broadband
measurements, finite sampling, and disturbances such as atmospheric seeing and
detector readout noise are also investigated. The methods presented here can be
used to compare the precision limits of various devices for measuring phase
steps and for optimising the parameters of the devices. Under ideal conditions
the Shack-Hartmann and the Foucault devices nearly attain the ultimate quantum
statistical limits, whereas the Mach-Zehnder and the curvature devices each
require approximately twenty times as many photons in order to reach the same
precision.Comment: 23 pages, 19 figures, to be submitted to Journal of Modern Optic
Staggered Chiral Perturbation Theory and the Fourth-Root Trick
Staggered chiral perturbation theory (schpt) takes into account the
"fourth-root trick" for reducing unwanted (taste) degrees of freedom with
staggered quarks by multiplying the contribution of each sea quark loop by a
factor of 1/4. In the special case of four staggered fields (four flavors,
nF=4), I show here that certain assumptions about analyticity and phase
structure imply the validity of this procedure for representing the rooting
trick in the chiral sector. I start from the observation that, when the four
flavors are degenerate, the fourth root simply reduces nF=4 to nF=1. One can
then treat nondegenerate quark masses by expanding around the degenerate limit.
With additional assumptions on decoupling, the result can be extended to the
more interesting cases of nF=3, 2, or 1. A apparent paradox associated with the
one-flavor case is resolved. Coupled with some expected features of unrooted
staggered quarks in the continuum limit, in particular the restoration of taste
symmetry, schpt then implies that the fourth-root trick induces no problems
(for example, a violation of unitarity that persists in the continuum limit) in
the lowest energy sector of staggered lattice QCD. It also says that the theory
with staggered valence quarks and rooted staggered sea quarks behaves like a
simple, partially-quenched theory, not like a "mixed" theory in which sea and
valence quarks have different lattice actions. In most cases, the assumptions
made in this paper are not only sufficient but also necessary for the validity
of schpt, so that a variety of possible new routes for testing this validity
are opened.Comment: 39 pages, 3 figures. v3: minor changes: improved explanations and
less tentative discussion in several places; corresponds to published versio
Decoherence induced by Smith-Purcell radiation
The interaction between charged particles and the vacuum fluctuations of the
electromagnetic field induces decoherence, and therefore affects the contrast
of fringes in an interference experiment. In this article we show that if a
double slit experiment is performed near a conducting grating, the fringe
visibility is reduced. We find that the reduction of contrast is proportional
to the number of grooves in the conducting surface, and that for realistic
values of the parameters it could be large enough to be observed. The effect
can be understood in terms of the Smith-Purcell radiation produced by the
surface currents induced in the conductor.Comment: 10 pages, 3 figures. Improved discussion on experimental
perspectives. References added. Version to appear in Phys. Rev.
Symmetry restoration in Hartree-Fock-Bogoliubov based theories
We present a pfaffian formula for projection and symmetry restoration for
wave functions of the general Bogoliubov form, including quasiparticle excited
states and linear combinations of them. This solves a long-standing problem in
calculating states of good symmetry, arising from the sign ambiguity of the
commonly used determinant formula. A simple example is given of projecting good
particle number and angular momentum from a Bogoliubov wave function in the
Fock space of a single j-shell.Comment: 5 pages and 1 table, revised version include more general result
Frenet-Serret dynamics
We consider the motion of a particle described by an action that is a
functional of the Frenet-Serret [FS] curvatures associated with the embedding
of its worldline in Minkowski space. We develop a theory of deformations
tailored to the FS frame. Both the Euler-Lagrange equations and the physical
invariants of the motion associated with the Poincar\'e symmetry of Minkowski
space, the mass and the spin of the particle, are expressed in a simple way in
terms of these curvatures. The simplest non-trivial model of this form, with
the lagrangian depending on the first FS (or geodesic) curvature, is
integrable. We show how this integrability can be deduced from the Poincar\'e
invariants of the motion. We go on to explore the structure of these invariants
in higher-order models. In particular, the integrability of the model described
by a lagrangian that is a function of the second FS curvature (or torsion) is
established in a three dimensional ambient spacetime.Comment: 20 pages, no figures - replaced with version to appear in Class.
Quant. Grav. - minor changes, added Conclusions sectio
Dynamics of the Fisher Information Metric
We present a method to generate probability distributions that correspond to
metrics obeying partial differential equations generated by extremizing a
functional , where is the
Fisher metric. We postulate that this functional of the dynamical variable
is stationary with respect to small variations of these
variables. Our approach enables a dynamical approach to Fisher information
metric. It allows to impose symmetries on a statistical system in a systematic
way. This work is mainly motivated by the entropy approach to nonmonotonic
reasoning.Comment: 11 page
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