Discrete and Continuum Third Quantization of Gravity (original) (raw)

Related papers

A new class of group field theories for first order discrete quantum gravity

Classical and Quantum Gravity, 2008

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches. * d.oriti@phys.uu.nl † t.tlas@damtp.cam.ac.uk the purely topological case or for very special choices of observables, a sum over all the histories between given spin network states. At present, group field theories are the only known tool to define uniquely such sum over spin foams, i.e. with fully specified weights, in a perturbative expansion of the GFT partition function. In this property, lies the main reason of interest in GFTs, from the LQG perspective. And indeed, up to now, group field theories have been mainly considered and used just as such: as a tool to define a sum over spin foams with prescribed weights, i.e. as an auxiliary formalism to define/construct spin foam models.

Cosmology from Group Field Theory Formalism for Quantum Gravity

Physical Review Letters, 2013

We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.

Group field theories for all loop quantum gravity

New Journal of Physics, 2015

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

Group Field Theory: An Overview

International Journal of Theoretical Physics - INT J THEOR PHYS, 2005

We give a brief overview of the properties of a higher-dimensional generalization of matrix model which arise naturally in the context of a background approach to quantum gravity, the so-called group field theory. We show in which sense this theory provides a third quantization point-of-view on quantum gravity.

A group field theory for 3d quantum gravity coupled to a scalar field

We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of this model are given by Riemannian quantum gravity spin foam amplitudes coupled to a scalar matter field. We briefly discuss the features of this model and its possible generalisations. *

Group field theory formulation of 3D quantum gravity coupled to matter fields

Classical and Quantum Gravity, 2006

We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU (2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss.

Group field cosmology: a cosmological field theory of quantum geometry

Classical and Quantum Gravity, 2012

Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.

Comparative quantizations of (2+1)-dimensional gravity

Physical review D: Particles and fields, 1995

We compare three approaches to the quantization of (2+1)dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the "frozen time" holonomy formulation. * email: carlip@dirac.ucdavis.edu † email: nelson@to.infn.it * We use standard ADM notation: g ij and R refer to the induced metric and scalar curvature of a time slice, while the spacetime metric and curvature are denoted (3) g µν and (3) R. † In the mathematics literature, the modulus is usually denoted by τ . Following Moncrief [2], however, we have already used τ to denote the York time coordinate.

Dual loop quantizations of 3d gravity

arXiv: General Relativity and Quantum Cosmology, 2018

The loop quantization of 3d gravity consists in defining the Hilbert space of states satisfying the Gau{\ss} constraint and the flatness constraint. The Gau{\ss} constraint is enforced at the kinematical level by introducing spin networks which form a basis for the Hilbert space of gauge invariant functionals. The flatness constraint is implemented at the dynamical level via the Ponzano-Regge state-sum model. We propose in this work a dual loop quantization scheme where the role of the constraints is exchanged. The flatness constraint is imposed first via the introduction of a new basis labeled by group variables, while the Gau{\ss} constraint is implemented dynamically using a projector which is related to the Dijkgraaf-Witten model. We discuss how this alternative quantization program is related to 3d teleparallel gravity.

Equivalent quantizations of (2+1)-dimensional gravity

1994

We compare three approaches to the quantization of (2+1)dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the “frozen time ” holonomy formulation.