955 research outputs found
Emergent discrete time and quantization: relativistic particle with extradimensions
We study the reparametrization invariant system of a classical relativistic
particle moving in (5+1) dimensions, of which two internal ones are
compactified to form a torus. A discrete physical time is constructed based on
a quasi-local invariant observable. Due to ergodicity, it is simply related to
the proper time on average. The external motion in Minkowski space can then be
described as a unitary quantum mechanical evolution.Comment: 13 pages, 6 figures; replaced with embedded figures and fixed layou
Linear constraints from generally covariant systems with quadratic constraints
How to make compatible both boundary and gauge conditions for generally
covariant theories using the gauge symmetry generated by first class
constraints is studied. This approach employs finite gauge transformations in
contrast with previous works which use infinitesimal ones. Two kinds of
variational principles are taken into account; the first one features
non-gauge-invariant actions whereas the second includes fully gauge-invariant
actions. Furthermore, it is shown that it is possible to rewrite fully
gauge-invariant actions featuring first class constraints quadratic in the
momenta into first class constraints linear in the momenta (and homogeneous in
some cases) due to the full gauge invariance of their actions. This shows that
the gauge symmetry present in generally covariant theories having first class
constraints quadratic in the momenta is not of a different kind with respect to
the one of theories with first class constraints linear in the momenta if fully
gauge-invariant actions are taken into account for the former theories. These
ideas are implemented for the parametrized relativistic free particle,
parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the
corrections to many misprints of v1 and also the ones of the published
version. The conceptual and technical parts of the paper are not altere
A topological limit of gravity admitting an SU(2) connection formulation
We study the Hamiltonian formulation of the generally covariant theory
defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad
field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This
theory can be thought of as the limit of the Holst action for gravity for the
Newton constant G goes to infinity and Immirzi parameter goes to zero, while
keeping their product fixed. This theory has for a long time been conjectured
to be topological. We prove this statement both in the covariant phase space
formulation as well as in the standard Dirac formulation. In the time gauge,
the unconstrained phase space of theory admits an SU(2) connection formulation
which makes it isomorphic to the unconstrained phase space of gravity in terms
of Ashtekar-Barbero variables. Among possible physical applications, we argue
that the quantization of this topological theory might shed new light on the
nature of the degrees of freedom that are responsible for black entropy in loop
quantum gravity.Comment: Appendix added where moldels leading to boundary degrees of freedom
are constructed. This version will appear in PRD
Quantum mechanics without spacetime II : noncommutative geometry and the free point particle
In a recent paper we have suggested that a formulation of quantum mechanics
should exist, which does not require the concept of time, and that the
appropriate mathematical language for such a formulation is noncommutative
differential geometry. In the present paper we discuss this formulation for the
free point particle, by introducing a commutation relation for a set of
noncommuting coordinates. The sought for background independent quantum
mechanics is derived from this commutation relation for the coordinates. We
propose that the basic equations are invariant under automorphisms which map
one set of coordinates to another- this is a natural generalization of
diffeomorphism invariance when one makes a transition to noncommutative
geometry. The background independent description becomes equivalent to standard
quantum mechanics if a spacetime manifold exists, because of the proposed
automorphism invariance. The suggested basic equations also give a quantum
gravitational description of the free particle.Comment: 8 page
Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian
action principles that describe general relativity as a constrained BF theory
and that include the Immirzi parameter. The relation between these two
Lagrangian actions has been already studied through a map among the fields
involved. The main difference between these is the way the Immirzi parameter is
included, since in one of them the Immirzi parameter is included explicitly in
the BF terms, whereas in the other (the CMPR action) it is in the constraint on
the B fields. In this work we continue the analysis of their relationship but
at the Hamiltonian level. Particularly, we are interested in seeing how the
above difference appears in the constraint structure of both action principles.
We find that they both possess the same number of first-class and second-class
constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on
account of the type of canonical variables employed. The two algebras can be
transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure
Herschel observations of the circumstellar environment of the two Herbig Be stars R Mon and PDS27
We report and analyse FIR observations of two Herbig Be stars, R Mon and PDS
27, obtained with Herschel's instruments PACS and SPIRE. We construct SEDs and
derive the infrared excess. We extract line fluxes from the PACS and SPIRE
spectra and construct rotational diagrams in order to estimate the excitation
temperature of the gas. We derive CO, [OI] and [CI] luminosities to determine
physical conditions of the gas, as well as the dominant cooling mechanism. We
confirm that the Herbig Be stars are surrounded by remnants from their parental
clouds, with an IR excess that mainly originates in a disc. In R Mon we detect
[OI], [CI], [CII], CO (26 transitions), water and OH, while in PDS 27 we only
detect [CI] and CO (8 transitions). We attribute the absence of OH and water in
PDS 27 to UV photo-dissociation and photo-evaporation. From the rotational
diagrams, we find several components for CO: we derive 94990 K,
35820 K & 7712 K for R Mon, 9612 K & 314 K for PDS 27 and
258 K & 276 K for their respective compact neighbours. The forsterite
feature at 69m was not detected in either of the sources, probably due to
the lack of (warm) crystalline dust in a flat disc. We find that cooling by
molecules is dominant in the Herbig Be stars, while this is not the case in
Herbig Ae stars where cooling by [OI] dominates. Moreover, we show that in the
Herbig Be star R Mon, outflow shocks are the dominant gas heating mechanism,
while in Herbig Ae stars this is stellar. The outflow of R Mon contributes to
the observed line emission by heating the gas, both in the central spaxel/beam
covering the disc and the immediate surroundings, as well as in those
spaxels/beams covering the parabolic shell around it. PDS 27, a B2 star, has
dispersed a large part of its gas content and/or destroyed molecules; this is
likely given its intense UV field.Comment: Accepted for publication in Astronomy & Astrophysic
On the Borromean arithmetic orbifolds
We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that
is arithmetic if and only if (m, n, p) is one of the 12 triples (3, 3, 3), (3, 3, â), (3, 4, 4), (3, 6, 6), (3, â, â), (4, 4, 4), (4, 4, â), (4, â, â), (6, 6, 6), (6, 6, â), (â, â, â). The main purpose of the paper is to present each Gmnp, arithmetic, as a group of 4 x 4 matrices with entries in the ring of integers of a totally real number field K, and which are automorphs of a quaternary form F with entries in K of Sylvester type (+, +, +, -)
Time boundary terms and Dirac constraints
Time boundary terms usually added to action principles are systematically
handled in the framework of Dirac's canonical analysis. The procedure begins
with the introduction of the boundary term into the integral Hamiltonian action
and then the resulting action is interpreted as a Lagrangian one to which
Dirac's method is applied. Once the general theory is developed, the current
procedure is implemented and illustrated in various examples which are
originally endowed with different types of constraints.Comment: 12 page
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