Simple model for quantum general relativity from loop quantum gravity (original) (raw)

A finite quantum gravity field theory model

Classical and Quantum Gravity, 2011

We discuss the quantization of delta gravity, a two symmetric tensors’ model of gravity. This model, in cosmology, shows accelerated expansion without a cosmological constant. We present the \tilde{\delta } transformation which defines the geometry of the model. Then, we show that all delta-type models live at one loop only. We apply this to general relativity and we calculate the one-loop divergent part of the effective action showing its null contribution in vacuum, implying a finite model. Then, we proceed to study the existence of ghosts in the model. Finally, we study the form of the finite quantum corrections to the classical action of the model.

Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity

Symmetry, Integrability and Geometry: Methods and Applications, 2012

We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.

Quantum-reduced loop gravity: Cosmology

Physical Review D, 2013

We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum-gravity model is the loop representation basis

We show that the Hilbert space basis that defines the Ponzano-Regge-Turaev-Viro-Ooguri combinatorial definition of 3-d Quantum Gravity is the same as the one that defines the Loop Representation. We show how to compute lengths in Witten's 3-d gravity and how to reconstruct the 2-d geometry from a state of Witten's theory. We show that the non-degenerate geometries are contained in the Witten's Hilbert space. We sketch an extension of the combinatorial construction to the physical 4-d case, by defining a modification of Regge calculus in which areas, rather than lengths, are taken as independent variables. We provide an expression for the scalar product in the Loop representation in 4-d. We discuss the general form of a nonperturbative quantum theory of gravity, and argue that it should be given by a generalization of Atiyah's topological quantum field theories axioms.

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.

Outline of a generally covariant quantum field theory and a quantum theory of gravity

We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the theory. We present the explicit calculation of the transition probability between two volume eigenstates as an example. We discuss the choices on which the T-theory relies, and the possibilities of modifying them.

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.

Quantum-reduced loop gravity: Relation with the full theory

Physical Review D, 2013

The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects states based on reduced graphs with Livine-Speziale coherent intertwiners and could simplify the analysis of the dynamics in the full theory.

Gravity quantized: Loop quantum gravity with a scalar field

2010

but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level. PACS numbers: 4.60.Pp; 04.60.-m; 03.65.Ta; 04.62.+v