arXiv subjects

Laurent Freidel

Publications and source records attributed to Laurent Freidel.

At least 91 records · Page 5Linked to original sources

arXiv2014

Quantum Gravity, Dynamical Phase Space and String Theory

In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase space and in which space-time is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The space-time and momentum space dynamics, and thus dynamical phase space, is governed by a new version of the Renormalization Group.

hep-th↗

arXiv2014

Spinning geometry = Twisted geometry

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space.

gr-qc↗

arXiv2013

Action and Vertices in the Worldine Formalism

Utilizing the worldline formalism we study the effects of demanding local interactions on the corresponding vertex factor. We begin by reviewing the familiar case of a relativistic particle in Minkowksi space, showing that localization gives rise to the standard conservation of momentum at each vertex. A generalization to curved geometry is then studied and a notion of covariant Fourier transform is introduced to aid in the analysis. The vertex factor is found to coincide with the one derived for flat spacetime. Next, we apply this formalism to a loop immersed in a gravitational field, demonstrating that the loop momenta is determined entirely by the external momenta. Finally, we postulate that the semi--classical effects of quantum gravity on the Feynman path integral can be accounted for by a modification to the vertex factor which de-localizes the vertex. We study one particular Lorentz invariant de-localization which, remarkably, has no effect on conservation of vertex momenta.

hep-th↗

arXiv2013

Scalar Field Theory in Curved Momentum Space

We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard $φ^3$--theory and the corresponding Feynman rules we modify them to account for the non--trivial geometry of momentum space. These modified rules are then used to reconstruct the generating functional and extract the action for the theory. A method for performing a covariant Fourier transform is then developed and applied to the action. We find that the transformed fields depend implicitly on a fixed point in momentum space with fields based at different points being related by a non-local transformation. The interaction term in the action is also non--local, but the kinetic term can be made local by choosing the base point to be the origin of momentum space.

hep-th↗

arXiv2013

Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics

We study the properties of gravitational system in finite regions bounded by gravitational screens. We present the detail construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy and viscous stress tensor, while the conservations are analogs of non-equilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and non-equilibrium thermodynamics.

gr-qc↗

arXiv2013

Born Reciprocity in String Theory and the Nature of Spacetime

After many years, the deep nature of spacetime in string theory remains an enigma. In this letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived dynamical concept. This viewpoint may be thought of as a dynamical chiral phase space formulation of string theory, in which Born reciprocity is implemented as a choice of a Lagrangian submanifold of the phase space, and amounts to a generalization of T-duality. In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invariance and the underlying string geometry should be understood in terms of dynamical bi-Lagrangian manifolds and an apparently new geometric structure, somewhat reminiscent of para-quaternionic geometry, which we call Born geometry.

hep-th↗

arXiv2013

Noisy soccer balls

In her Comment arXiv:1202.4066 [hep-th] Hossenfelder proposes a generalization of the results we reported in Phys. Rev. D84 (2011) 087702 and argues that thermal fluctuations introduce incurable pathologies for the description of macroscopic bodies in the relative-locality framework. We here show that Hossenfelder's analysis, while raising a very interesting point, is incomplete and leads to incorrect conclusions. Her estimate for the fluctuations did not take into account some contributions from the geometry of momentum space which must be included at the relevant order of approximation. Using the full expression here derived one finds that thermal fluctuations are not in general large for macroscopic bodies in the relative-locality framework. We find that such corrections can be unexpectedly large only for some choices of momentum-space geometry, and we comment on the possibility of developing a phenomenology suitable for possibly ruling out such geometries of momentum space.

hep-th↗

arXiv2013

A Discrete and Coherent Basis of Intertwiners

We construct a new discrete basis of 4-valent SU(2) intertwiners. This basis possesses both the advantage of being discrete, while at the same time representing accurately the classical degrees of freedom; hence it is coherent. The closed spin network amplitude obtained from these intertwiners depends on twenty spins and can be evaluated by a generalization of the Racah formula for an arbitrary graph. The asymptotic limit of these amplitudes is found. We give, for the first time, the asymptotics of 15j symbols in the real basis. Remarkably it gives a generalization of the Regge action to twisted geometries.

math-ph↗

arXiv2013

Continuous formulation of the Loop Quantum Gravity phase space

In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux variables. Our construction shows that the fluxes depend on the three-geometry, but also explicitly on the connection, explaining their non commutativity. It also clearly shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. This allows us to resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since we establish that both geometries belong to the same equivalence class. This finally gives us a clear understanding of the relationship between the piecewise flat spin foam geometries and Regge geometries, which are only piecewise-linear flat: While Regge geometry corresponds to metrics whose curvature is concentrated around straight edges, the loop gravity geometry correspond to metrics whose curvature is concentrated around not necessarily straight edges.

gr-qc↗

arXiv2012

On the Relations between Gravity and BF Theories

We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their generalizations, and the MacDowell-Mansouri action.

gr-qc↗

arXiv2012

OPERA neutrinos and relativity

In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to loose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres and Bi et. al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these anomalous processes are forbidden if Lorentz symmetry is instead "deformed", preserving the relativity of inertial frames. These deformations add non-linear terms to energy momentum relations, conservation laws and Lorentz transformations in a way that is consistent with the relativity of inertial observers.

hep-ph↗

arXiv2012

Holomorphic Lorentzian Simplicity Constraints

We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d spacelike polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.

gr-qc↗

arXiv2012

New tools for Loop Quantum Gravity with applications to a simple model

Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field at large scales. Here we will review the recent U(N) framework for Loop Quantum Gravity and the new spinor representation (that provides a classical setting for the U(N) framework). Then, we will apply these techniques to a simple model in order to propose a dynamics for a symmetry reduced sector of the theory. Furthermore, we will explore certain analogies of this model with Loop Quantum Cosmology.

gr-qc↗

arXiv2012

On the exact evaluation of spin networks

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs.

gr-qc↗

arXiv2011

Dynamics for a simple graph using the U(N) framework for loop quantum gravity

The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an interesting global U(N) symmetry in this model that selects the homogeneous/isotropic sector. Then, we propose a quantum Hamiltonian operator for this reduced sector. Finally, we introduce the spinor representation for LQG in order to propose a classical effective dynamics for this model.

gr-qc↗

arXiv2011

The Hamiltonian constraint in 3d Riemannian loop quantum gravity

We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn-Elliott (pentagon) identity. This fills the gap between the canonical quantization and the symmetries of the Ponzano-Regge state-sum model for 3d gravity.

gr-qc↗

arXiv2011

Relative locality: A deepening of the relativity principle

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $\hbar$ and $G_N$ may be neglected, while their ratio, the Planck mass $M_p =\sqrt{\hbar / G_N}$, is important. We propose that $M_p$ governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.

hep-th↗

arXiv2011

Relative locality and the soccer ball problem

We consider the behavior of macroscopic bodies within the framework of relative locality, which is a recent proposal for Planck scale modifications of the relativistic dynamics of particles which are described as arising from deformations in the geometry of momentum space. These lead to the addition of non-linear terms to the energy-momentum relations and conservation laws, which are suppressed by powers of ratio between the energy E of the particles involved and the Planck mass M_P. We consider and resolve a common objection against such proposals, which is that, even if the corrections are small for elementary particles in current experiments, they are huge when applied to composite systems such as soccer balls, planets and stars, with energies E_{macro} much larger than M_P. We show that this "soccer-ball problem" does not arise within the framework of relative locality, because the non-linear effects for the dynamics of a composite system with N elementary particles appear at most of order E_{macro}/ N M_{P}.

hep-th↗