Diffeomorphisms in group field theories

Baratin, Aristide; Girelli, Florian; Oriti, Daniele

doi:10.1103/physrevd.83.104051

Cited by 90 publications

(190 citation statements)

References 64 publications

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“…Third quantization of loop quantum gravity has led to the development of group field theory [33,34,35,36]. Recently, group field cosmology has also been developed [37,38].…”

Section: Resultsmentioning

confidence: 99%

Fourth quantization

Faizal¹

2013

Physics Letters B

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In this paper we will analyse the creation of the multiverse. We will first calculate the wave function for the multiverse using third quantization. Then we will fourth quantize this theory. We will show that there is no single vacuum state for this theory. Thus, we can end up with a multiverse, even after starting from a vacuum state. This will be used as a possible explanation for the creation of the multiverse. We also analyse the effect of interactions in this fourth quantized theory.

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“…Third quantization of loop quantum gravity has led to the development of group field theory [33,34,35,36]. Recently, group field cosmology has also been developed [37,38].…”

Section: Resultsmentioning

confidence: 99%

Fourth quantization

Faizal¹

2013

Physics Letters B

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“…Despite various difficulties 8 and the rather slow development since the introduction of tensor models, some interesting results have been reported recently [9][10][11][12][13][14][15] . These developments strengthen the general belief that tensor models indicate the right direction to the background independent formulation of quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

“…The antisymmetry of the first two entries (15), the cyclic identity (30), and the fundamental identity (48) shows that the coordinatesx µ and the 3-ary product (14) form a Lie triple system [27][28][29]43 . A Lie triple system is known to have an associated Lie algebra, and the same Lie triple system as the present case is explained in detail as an example in Ref.…”

Section: The 3-ary Product Of Coordinates and Snyder's Noncommutmentioning

confidence: 99%

Tensor models and 3-ary algebras

Sasakura¹

2011

Journal of Mathematical Physics

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Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.

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“…In the recent years, non-commutative techniques entered the game thanks to a new type of Fourier transform [7][8][9][10][11]. The general mathematical formalism behind this generalized Fourier transform was mostly developed by Majid [12] and it was rediscovered later on in the context of 3d spinfoam while coupling particles to the Ponzano-Regge model [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…This non-commutative perspective for spinfoams allows to connect the diffeomorphism symmetry (in 3d) of spinfoam amplitudes to quantum group symmetries of the field theory [11]. One can expect that these symmetries will be useful in order to discuss the question of renormalization of the field theory by putting constraints on the renormalization scheme and allowed counter-terms.…”

Section: Introductionmentioning

confidence: 99%

Spinors group field theory and Voros star product: First contact

2012

Self Cite

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In the context of non-commutative geometries, we develop a group Fourier transform for the Lie group SU(2). Our method is based on the Schwinger representation of the Lie algebra su(2) in terms of spinors. It allows us to prove that the non-commutative R 3 space dual to the SU(2) group is in fact of the Moyal-type and endowed with the Voros star-product when expressed in the spinor variables. Finally, from the perspective of quantum gravity, we discuss the application of these new tools to group field theories for spinfoam models and their interpretation as non-commutative field theories with quantum-deformed symmetries.

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Diffeomorphisms in group field theories

Cited by 90 publications

References 64 publications

Fourth quantization

Fourth quantization

Tensor models and 3-ary algebras

Spinors group field theory and Voros star product: First contact

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