arXiv subjects

Florian Girelli

Publications and source records attributed to Florian Girelli.

At least 55 records · Page 3Linked to original sources

arXiv2010

Scalar field theory in Snyder space-time: alternatives

We construct two types of scalar field theory on Snyder space-time. The first one is based on the natural momenta addition inherent to the coset momentum space. This construction uncovers a non-associative deformation of the Poincaré symmetries. The second one considers Snyder space-time as a subspace of a larger non-commutative space. We discuss different possibilities to restrict the extra-dimensional scalar field theory to a theory living only on Sndyer space-time and present the consequences of these restrictions on the Poincaré symmetries. We show moreover how the non-associative approach and the Doplicher-Fredenhagen-Roberts space can be seen as specific approximations of the extra-dimensional theory. These results are obtained for the 3d Euclidian Snyder space-time constructed from $\SO(3,1)/\SO(3)$, but our results extend to any dimension and signature.

hep-th↗

arXiv2010

A Deformed Poincare Invariance for Group Field Theories

In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular Boulatov's theory reproduces the amplitudes of the Ponzano-Regge spinfoam model for 3d quantum gravity. Motivated by recent works on field theories on non-commutative flat spaces, we show that Boulatov's theory (and its colored version) is actually invariant under a global deformed Poincare symmetry. This allows to define a notion of flat/excited geometry states when considering scalar perturbations around classical solutions of the group field equations of motion. As a side-result, our analysis seems to point out that the notion of braiding of group field theories should be a key feature to study further in this context.

gr-qc↗

arXiv2009

Field theories with homogenous momentum space

We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in Snyder's space-time. As a side-product we identify a star product realization of Snyder's non-commutative space, but also the deformation of the Poincare symmetries necessary to have these symmetries realized in Snyder's space-time. A key feature of the construction is that the star product is non-associative.

hep-th↗

arXiv2009

Emergent gravitational dynamics in Bose-Einstein condensates

We discuss a toy model for an emergent non-relativistic gravitational theory. Within a certain class of Bose-Einstein condensates, it is possible to show that, in a suitable regime, a modified version of non-relativistic Newtonian gravity does effectively describes the low energy dynamics of the coupled system condensate/quasi-particles.

gr-qc↗

arXiv2009

Analogue Models for Emergent Gravity

Gravity stands out among the fundamental interactions because of its apparent incompatibility with having a quantum description. Moreover, thermodynamic aspects of gravitation theory appears as puzzling features of some classical solutions such as black holes. These and other aspects of gravitational theories have recently lead to the proposal that gravity might not be a fundamental interaction but rather an emergent phenomenon, a sort of hydrodynamic limit of some more fundamental theory. In order to further explore this possibility we shall here discuss two systems where such emergence of a gravitational dynamics is observed. We shall consider first the case of a non-relativistic Bose-Einstein condensate and then a more abstract model based on scalar fields living on a Riemannian manifold. This will allow us to put in evidence the general issues related to emergent gravity scenarios with a particular attention to the role and nature of Lorentz and diffeomorphism invariance.

gr-qc↗

arXiv2009

Is the notion of time really fundamental?

From the Physics point of view, time is now best described through General Relativity, as part of space-time which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics, quantum mechanical effects... This irreversibility can look puzzling since time-like loops (and hence time machines) can appear in General Relativity (for example in the Goedel universe, a solution of Einstein's equations). We take this apparent discrepancy as a warning bell pointing to us that time as we understand it, might not be fundamental and that whatever theory, lying beyond General Relativity, may not include time as we know it as a fundamental structure. We propose therefore, following the philosophy of analog models of gravity, that time and gravity might not be fundamental per se, but only emergent features. We illustrate our proposal using a toy-model where we show how the Lorentzian signature and Nordstroem gravity (a diffeomorphisms invariant scalar gravity theory) can emerge from a timeless non-dynamical space.

gr-qc↗

arXiv2009

4d Deformed Special Relativity from Group Field Theories

We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF-theory in 4 space-time dimensions. This is done at a non-perturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the non-commutative field theory governs their effective dynamics.

gr-qc↗

arXiv2009

On the emergence of Lorentzian signature and scalar gravity

In recent years, a growing momentum has been gained by the emergent gravity framework. Within the latter, the very concepts of geometry and gravitational interaction are not seen as elementary aspects of Nature but rather as collective phenomena associated to the dynamics of more fundamental objects. In this paper we want to further explore this possibility by proposing a model of emergent Lorentzian signature and scalar gravity. Assuming that the dynamics of the fundamental objects can give rise in first place to a Riemannian manifold and a set of scalar fields we show how time (in the sense of hyperbolic equations) can emerge as a property of perturbations dynamics around some specific class of solutions of the field equations. Moreover, we show that these perturbations can give rise to a spin-0 gravity via a suitable redefinition of the fields that identifies the relevant degrees of freedom. In particular, we find that our model gives rise to Nordstrom gravity. Since this theory is invariant under general coordinate transformations, this also shows how diffeomorphism invariance (albeit of a weaker form than the one of general relativity) can emerge from much simpler systems.

gr-qc↗

arXiv2008

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.

gr-qc↗

arXiv2007

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.

gr-qc↗

arXiv2007

Non-Commutativity of Effective Space-Time Coordinates and the Minimal Length

Considering that a position measurement can effectively involve a momentum-dependent shift and rescaling of the "true" space-time coordinates, we construct a set of effective space-time coordinates which are naturally non-commutative. They lead to a minimum length and are shown to be related to Snyder's coordinates and the five-dimensional formulation of Deformed Special Relativity. This effective approach then provides a natural physical interpretation for both the extra fifth dimension and the deformed momenta appearing in this context.

hep-th↗

arXiv2007

Planck-scale modified dispersion relations and Finsler geometry

A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined ``rainbow metric". We show here that the latter actually corresponds to a Finsler Geometry, the natural generalization of Riemannian Geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or Deformed Special Relativity-like models.

gr-qc↗

arXiv2007

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.

hep-th↗

arXiv2006

Some comments on the universal constant in DSR

Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to avoid some fundamental problems (e.g. soccer ball problem), we argue that we should switch point of view and consider instead the Newton constant $G$ as the universal constant.

gr-qc↗

arXiv2005

Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.

gr-qc↗

arXiv2005

Holonomic quantum computation in the presence of decoherence

We present a scheme to study non-abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.

quant-ph↗

arXiv2004

Physics of Deformed Special Relativity

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Unfortunately DSR is up to now plagued by many conceptual problems (in particular how it describes macroscopic objects) which forbids a definitive physical interpretation and clear predictions. Here we propose a consistent framework to interpret DSR. We extend the principle of relativity: the same way that Special Relativity showed us that the definition of a reference frame requires to specify its speed, we show that DSR implies that we must also take into account its mass. We further advocate a 5-dimensional point of view on DSR physics and the extension of the kinematical symmetry from the Poincare group to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the concept of a pentamomentum and to take into account the renormalization of the DSR deformation parameter kappa. This allows the resolution of the "soccer ball problem" (definition of many-particle-states) and provides a physical interpretation of the non-commutativity and non-associativity of the addition the relativistic quadrimomentum.

gr-qc↗

arXiv2004

Physics of Deformed Special Relativity: Relativity Principle revisited

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Some experiments will soon be able to test some low energy effects of quantum gravity, and DSR is a very promising candidate to describe these latter. Unfortunately DSR is up to now plagued by many conceptual problems (in particular how it describes macroscopic objects) which forbids a definitive physical interpretation and clear predictions. Here we propose a consistent framework to interpret DSR. We extend the principle of relativity: the same way that Special Relativity showed us that the definition of a reference frame requires to specify its speed, we show that DSR implies that we must also take into account its mass. We further advocate a 5-dimensional point of view on DSR physics and the extension of the kinematical symmetry from the Poincare group to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the concept of a pentamomentum and to take into account the renormalization of the DSR deformation parameter kappa. This allows the resolution of the "soccer ball problem" (definition of many-particle-states) and provides a physical interpretation of the non-commutativity and non-associativity of the addition the relativistic quadrimomentum. In particular, the coproduct of the kappa-Poincare algebra is interpreted as defining the law of change of reference frames and not the law of scattering. This point of view places DSR as a theory, half-way between Special Relativity and General Relativity, effectively implementing the Schwarzschild mass bound in a flat relativistic context.

gr-qc↗