Group field theories for all loop quantum gravity

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

doi:10.1088/1367-2630/17/2/023042

Cited by 62 publications

(96 citation statements)

References 115 publications

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“…The whole description of the coupled system would thus be purely algebraic and combinatorial. Indeed, this can be realised consistently for any type of matter field [36]. However, in 3d life is made easier by the topological nature of gravity and by the fact that one can describe matter as a topological defect.…”

Section: Assorted Questions For the Present But Especially For The Fmentioning

confidence: 97%

Quantum Gravity as a Quantum Field Theory of Simplicial Geometry

Oriti

Quantum Gravity

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122

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Section: Assorted Questions For the Present But Especially For The Fmentioning

confidence: 97%

Quantum Gravity as a Quantum Field Theory of Simplicial Geometry

Oriti

Quantum Gravity

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122

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“…The main strategy that has been followed starts from the definition of spin foam amplitudes, encoding them in a GFT model. This has been mainly done in a simplicial context [1] (but see [15]). …”

Section: The Quantum Dynamicsmentioning

confidence: 99%

“…The same models can be straightforwardly extended to combinatorial settings more general than the simplicial one [15,35], but the geometric features of such generalised constructions are not yet fully understood. The first example is the version of the EPRL model [13,33], resulting from a specific choice of imposing the constraints in the representation variables, and only at the level of the GFT kinetic term:…”

Section: The Quantum Dynamicsmentioning

confidence: 99%

Group Field Theory and Loop Quantum Gravity

Oriti

2017

100 Years of General Relativity

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113

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We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a perspective on future developments. GFT FROM LQG PERSPECTIVE: THE GENERAL IDEAIn this contribution, we introduce the group field theory (GFT) formalism for quantum gravity [1], mainly from the point of view of loop quantum gravity, arguing why it represents, in our opinion, a most promising setting for future developments. We describe the kinematical Hilbert space and its relation to the LQG one, and how the GFT quantum dynamics connects to the canonical one as well as completes spin foam models. We also discuss the problem of defining the continuum limit of such theories and of extracting effective continuum physics, highlighting the important role that GFTs can play in this respect. This is not an in-depth introduction, nor a complete review of the literature. We only outline the foundations of the formalism, survey recent results and offer a perspective on future developments.An historical prelude -Group field theories can be approached from different angles, coming from different lines of research in quantum gravity. Historically, their first appearance [2,3] came as a development of tensor models [4] (themselves a generalisation of matrix models [5], which provided a successful quantisation of (pure) 2d gravity), allowing to make contact with state sum formulations of 3d quantum gravity (Ponzano-Regge and Turaev-Viro model), whose relation with simplicial quantum gravity, e.g. quantum Regge calculus [6], was already known, and more generally topological BF theory in any dimension. These first models were obtained by taking the simplest tensor model for 3d simplicial gravity and: 1) replacing the domain set for the tensor indices with a group manifold (SU (2)); 2) adding a gauge invariance property to the field (tensor), with the effect of introducing a gauge connection on the lattices generated by the perturbative expansion of the model. The triviality of the kinetic and interaction kernels (simple delta functions on the group) in the GFT action resulted in the amplitudes being exactly those of BF theory discretised on the same lattices (imposing flatness of the connection). Written in terms of group representations, the same amplitudes took the form of the mentioned state sums. This is the first way to understand group field theories: GFTs can be seen as tensor models enriched by algebraic data with a quantum geometric interpretation (allowing a nice encoding of discrete gravity degrees of freedom), or, equivalently, as more general class of combinatorially non-local field theories of tensorial type. The relation between state sum models of topological field theory, and their GFT formulation, and loop quantum gravity was soon pointed out in [7] (where the link to the dynamical triangulations approach [8] was also mentioned): the boundary states of such models matched the newly...

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“…In the rest of this article, we use results from the previous sections to outline a framework for equilibrium statistical mechanics for candidate quanta of geometry (along the lines presented in [14,15], but generalising further to a richer combinatorics based on [35]), and within it give an overview of some concrete examples. In particular, we show that a group field theory can be understood as an effective statistical field theory derived from a coarse-graining of a generalised Gibbs configuration of the underlying quanta.…”

Section: Equilibrium Statistical Mechanics In Quantum Gravitymentioning

confidence: 99%

Thermal Quantum Spacetime

Kotecha

2019

Universe

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The intersection of thermodynamics, quantum theory and gravity has revealed many profound insights, all the while posing new puzzles. In this article, we discuss an extension of equilibrium statistical mechanics and thermodynamics potentially compatible with a key feature of general relativity, background independence; and we subsequently use it in a candidate quantum gravity system, thus providing a preliminary formulation of a thermal quantum spacetime. Specifically, we emphasise on an information-theoretic characterisation of generalised Gibbs equilibrium that is shown to be particularly suited to background independent settings, and in which the status of entropy is elevated to being more fundamental than energy. We also shed light on its intimate connections with the thermal time hypothesis. Based on this we outline a framework for statistical mechanics of quantum gravity degrees of freedom of combinatorial and algebraic type, and apply it in several examples. In particular, we provide a quantum statistical basis for the origin of covariant group field theories, shown to arise as effective statistical field theories of the underlying quanta of space in a certain class of generalised Gibbs states. CONTENTS

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Group field theories for all loop quantum gravity

Cited by 62 publications

References 115 publications

Quantum Gravity as a Quantum Field Theory of Simplicial Geometry

Quantum Gravity as a Quantum Field Theory of Simplicial Geometry

Group Field Theory and Loop Quantum Gravity

Thermal Quantum Spacetime

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