Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory

Freidel, Laurent; Livine, Etera R.

doi:10.1088/0264-9381/23/6/012

Cited by 228 publications

(555 citation statements)

References 43 publications

Supporting

Mentioning

534

Contrasting

Order By: Relevance

“…The transformation between these two bases is therefore a generalized Fourier transform. A related duality transform, but involving expectation values of geometric observables in three-and four-dimensional state sum models, has been discussed in [39,[53][54][55][56]. Here we also find that the spectra of both kinds of Wilson loops coincide, revealing a deep self-duality.…”

Section: Jhep05(2017)123supporting

confidence: 64%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.This work has important applications for quantum gravity as well as the theory of topological phases in (3 + 1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably.We in particular show that the fusion bases of the (2 + 1)-dimensional theory lead to a rich set of bases for the (3 + 1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

show abstract

Section: Jhep05(2017)123supporting

confidence: 64%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The representations of a group are the objects of a category, and this sort of category can be used to build 'spin foam models' of background-free quantum field theories [5,6]. This endeavor has been most successful with 3d quantum gravity [49][50][51], but everyone working on this subject dreams of doing something similar for 4d quantum gravity [80]. Going from groups to 2-groups boosts the dimension of everything: the representations of a 2-group are the objects of a 2-category, and Crane and Sheppeard outlined a program for building a 4-dimensional spin foam model starting from the 2-category of representations of the Poincaré 2-group [37].…”

Section: The Poincaré 2-groupmentioning

confidence: 99%

“…See the paper by Baez et al [10] for a quick overview, and the work of Freidel, Louapre and Baratin for a deep treatment of the details [22,[49][50][51].…”

Section: In Dimension 4 B Is a G-valued 2-form-and Thanks To The Secmentioning

confidence: 99%

An invitation to higher gauge theory

2010

View full text Add to dashboard Cite

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincaré 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group', and the Lie 3-superalgebra that governs 11-dimensional supergravity.

show abstract

“…An example of this more general class is provided by the κ-deformed space [3,4,5], which is based on a Lie algebra type noncommutativity. Apart from its algebraic aspects [6,7,8,9,10,11], various features of field theories and symmetries on κ-deformed spaces have recently been studied [12,13,14,15,16]. Such a space has also been discussed in the context of doubly special relativity [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Twisted statistics inκ-Minkowski spacetime

et al. 2008

View full text Add to dashboard Cite

We consider the issue of statistics for identical particles or fields in κ-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription. I. INTRODUCTIONNoncommutative geometry is a plausible candidate for describing physics at the Planck scale, a simple model of which is given by the Moyal plane [1]. The models of noncommutative spacetime that follow from combining general relativity and uncertainty principle can be much more general [2]. An example of this more general class is provided by the κ-deformed space [3,4,5], which is based on a Lie algebra type noncommutativity. Apart from its algebraic aspects [6,7,8,9,10,11], various features of field theories and symmetries on κ-deformed spaces have recently been studied [12,13,14,15,16]. Such a space has also been discussed in the context of doubly special relativity [17,18,19].The issue of particle statistics plays a central role in the quantum description of a many-body system or field theory. This issue has naturally arisen in the context of noncommutative quantum mechanics and field theory [20,21,22,23,24]. In the noncommutative case, the issue of statistics is closely related to the symmetry of the noncommutative spacetime on which the dynamics is being studied. If a symmetry acts on a noncommutative spacetime, its coproduct usually has to be twisted in order to make the symmetry action compatible with the algebraic structure. In the commutative case, particle statistics is superselected, i.e. it is preserved under the action of the symmetry. In the presence of noncommutativity, it is thus natural to demand that the statistics is invariant under the action of the twisted symmetry. This condition leads to a new twisted flip operator, which is compatible with the twisted coproduct of the symmetry group [22,23]. The operators projecting to the symmetric and antisymmetric sectors of the Hilbert space are then constructed from the twisted flip operator. While most of the discussion of statistics in the noncommutative setup has been done in the context of the Moyal plane, some related ideas for κ-deformed spaces have also appeared recently [25,26,27].In this paper we set up a general formalism to describe statistics in κ-deformed spaces. Our formalism presented here is applicable to a system with an arbitrary symmetry group, which may include Poincare, Lorentz, Euclidean * trg@imsc.res.in † kumars.gupta@saha.ac.in ‡ harisp@uohyd.ernet.in § meljanac@irb.hr ¶ dmeljan@irb.hr

show abstract

Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory

Cited by 228 publications

References 43 publications

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

An invitation to higher gauge theory

Twisted statistics inκ-Minkowski spacetime

Contact Info

Product

Resources

About