The Relativistic Particle: Dirac observables and Feynman propagator

We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead to a structure very similar to the non-commutative geometry of Deformed Special Relativity (DSR). In this framework, it appears natural to consider the 4d relativistic particle as a five dimensional massless particle. We study its quantization in terms of wave functions on the 5d light cone. We introduce the corresponding five-dimensional action principle and analyze how it reproduces the physics of the 4d relativistic particle. The formalism is naturally subject to divergences and we show that DSR arises as a natural regularization: the 5d light cone is regularized as the de Sitter space. We interpret the fifth coordinate as the particle's proper time while the fifth moment can be understood as the mass. Finally, we show how to formulate the Feynman propagator and the Feynman amplitudes of quantum field theory in this context in terms of Dirac observables. This provides new insights for the construction of observables and scattering amplitudes in DSR.Comment: 14 pages, Revtex

Quantum reference frames and deformed symmetries

In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system undergoes an unavoidable measurement "back-action" that modifies its properties. In a quantum-gravitational setting, it has been argued that such a back-action may produce effects that are described at an effective level as a form of deformed (or doubly) special relativity. We examine this possibility using a simple constrained system that has been extensively studied in the context of quantum information. While our conclusions support the idea of a symmetry deformation, they also reveal a host of other effects that may be relevant to the context of quantum gravity, and could potentially conceal the symmetry deformation.Comment: 11 pages, revtex. Comments are welcom

Continuum spin foam model for 3d gravity

An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a {\em renormalized} sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e. g. triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is {\em projectively} equivalent to the Turaev-Viro model.Comment: 12 pages, 3 figure

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited

Gravitational dynamics in Bose Einstein condensates

Analogue models for gravity intend to provide a framework where matter and gravity, as well as their intertwined dynamics, emerge from degrees of freedom that have a priori nothing to do with what we call gravity or matter. Bose Einstein condensates (BEC) are a natural example of analogue model since one can identify matter propagating on a (pseudo-Riemannian) metric with collective excitations above the condensate of atoms. However, until now, a description of the "analogue gravitational dynamics" for such model was missing. We show here that in a BEC system with massive quasi-particles, the gravitational dynamics can be encoded in a modified (semi-classical) Poisson equation. In particular, gravity is of extreme short range (characterized by the healing length) and the cosmological constant appears from the non-condensed fraction of atoms in the quasi-particle vacuum. While some of these features make the analogue gravitational dynamics of our BEC system quite different from standard Newtonian gravity, we nonetheless show that it can be used to draw some interesting lessons about "emergent gravity" scenarios.Comment: Replaced with published version. 15 pages, no figures, revtex4. Reference adde

An anisotropic distribution of spin vectors in asteroid families

Current amount of ~500 asteroid models derived from the disk-integrated photometry by the lightcurve inversion method allows us to study not only the spin-vector properties of the whole population of MBAs, but also of several individual collisional families. We create a data set of 152 asteroids that were identified by the HCM method as members of ten collisional families, among them are 31 newly derived unique models and 24 new models with well-constrained pole-ecliptic latitudes of the spin axes. The remaining models are adopted from the DAMIT database or the literature. We revise the preliminary family membership identification by the HCM method according to several additional criteria - taxonomic type, color, albedo, maximum Yarkovsky semi-major axis drift and the consistency with the size-frequency distribution of each family, and consequently we remove interlopers. We then present the spin-vector distributions for eight asteroidal families. We use a combined orbital- and spin-evolution model to explain the observed spin-vector properties of objects among collisional families. In general, we observe for studied families similar trends in the (a_p, \beta) space: (i) larger asteroids are situated in the proximity of the center of the family; (ii) asteroids with \beta>0{\deg} are usually found to the right from the family center; (iii) on the other hand, asteroids with \beta<0{\deg} to the left from the center; (iv) majority of asteroids have large pole-ecliptic latitudes (|\beta|\gtrsim 30{\deg}); and finally (v) some families have a statistically significant excess of asteroids with \beta>0{\deg} or \beta<0{\deg}. Our numerical simulation of the long-term evolution of a collisional family is capable of reproducing well the observed spin-vector properties. Using this simulation, we also independently constrain the age of families Flora (1.0\pm0.5 Gyr) and Koronis (2.5-4 Gyr).Comment: Accepted for publication in A&A (September 16, 2013

The 1/N expansion of colored tensor models in arbitrary dimension

In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S^D contribute to the leading order in the large N limit.Comment: 4 pages, 3 figure

About Lorentz invariance in a discrete quantum setting

A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in the context of quantum gravity, the distance between two points becomes an operator and show through a toy model, inspired by Loop Quantum Gravity, that the notion of a quantum of geometry and of discrete spectra of geometric operators, is not inconsistent with Lorentz invariance. The main feature of the model is that a state of definite length for a given observer turns into a superposition of eigenstates of the length operator when seen by a boosted observer. More generally, we discuss the issue of actually measuring distances taking into account the limitations imposed by quantum gravity considerations and we analyze the notion of distance and the phenomenon of Lorentz contraction in the framework of ``deformed (or doubly) special relativity'' (DSR), which tentatively provides an effective description of quantum gravity around a flat background. In order to do this we study the Hilbert space structure of DSR, and study various quantum geometric operators acting on it and analyze their spectral properties. We also discuss the notion of spacetime point in DSR in terms of coherent states. We show how the way Lorentz invariance is preserved in this context is analogous to that in the toy model.Comment: 25 pages, RevTe

Hyperferritinemia without iron overload in patients with bilateral cataracts: a case series

Hepatologists and internists often encounter patients with unexplained high serum ferritin concentration. After exclusion of hereditary hemochromatosis and hemosiderosis, rare disorders like hereditary hyperferritinemia cataract syndrome should be considered in the differential diagnosis. This autosomal dominant syndrome, that typically presents with juvenile bilateral cataracts, was first described in 1995 and has an increasing number of recognized molecular defects within a regulatory region of the L-ferritin gene (FTL). CASE PRESENTATION: Two patients (32 and 49-year-old Caucasian men) from our ambulatory clinic were suspected as having this syndrome and a genetic analysis was performed. In both patients, sequencing of the FTL 5' region showed previously described mutations within the iron responsive element (FTL c.33 C > A and FTL c.32G > C). CONCLUSION: Hereditary hyperferritinemia cataract syndrome should be considered in all patients with unexplained hyperferritinemia without signs of iron overload, particularly those with juvenile bilateral cataracts. Liver biopsy and phlebotomy should be avoided in this disorder

Modified (A)dS Schwarzschild black holes in Rainbow spacetime

A modified (Anti-)de Sitter Schwarzschild black hole solution is presented in the framework of rainbow gravity with a cosmological constant. Its thermodynamical properties are investigated. In general the temperature of modified black holes is dependent on the energy of probes which take the measurement. However, a notion of intrinsic temperature can be introduced by identifying these probes with radiation particles emitted from black holes. It is interesting to find that the Hawking temperature of this sort of black holes can be reproduced by employing the extended uncertainty principle and modified dispersion relations to the ordinary (A)dS Schwarzschild black holes.Comment: 11 pages. The version to appear in CQ