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 $T_{rot}$ 949$\pm$90 K, 358$\pm$20 K & 77$\pm$12 K for R Mon, 96$\pm$12 K & 31$\pm$4 K for PDS 27 and 25$\pm$8 K & 27$\pm$6 K for their respective compact neighbours. The forsterite feature at 69$\mu$m 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, ∞), (3, 4, 4), (3, 6, 6), (3, ∞, ∞), (4, 4, 4), (4, 4, ∞), (4, ∞, ∞), (6, 6, 6), (6, 6, ∞), (∞, ∞, ∞). 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