Spin foam models of Yang Mills theory coupled to gravity (original) (raw)

Path integral representation of spin foam models of 4D gravity

Classical and Quantum Gravity, 2008

We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira & Rovelli (ELPR) and by Freidel & Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's & Livine's SO(4) projected states. For 0 ≤ γ < 1, the states can be restricted to SU(2) spin networks.

New Spin Foam Models of Quantum Gravity

Modern Physics Letters A, 2005

We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

Spin foam model for pure gauge theory coupled to quantum gravity

Physical Review D, 2002

We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a fourmanifold which is given merely combinatorially. The Riemannian Barrett-Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang-Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang-Mills scale.

A field-theoretic approach to Spin Foam models in Quantum Gravity

Proceedings of Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity — PoS(CNCFG2010)

We present an introduction to Group Field Theory models, motivating them on the basis of their relationship with discretized BF models of gravity. We derive the Feynmann rules and compute quantum corrections in the coherent states basis.

Spin-foams for all loop quantum gravity

Classical and Quantum Gravity, 2010

The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell spin-foams. The resulting framework admits all the spin-network states of loop quantum gravity, not only those defined by triangulations (or cubulations). In particular the notion of embedded spin-foam we use allows to consider knotting or linking spin-foam histories. Also the main tools as the vertex structure and the vertex amplitude are naturally generalized to arbitrary valency case. The correspondence between all the SU(2) intertwiners and the SU(2)×SU(2) EPRL intertwiners is proved to be 1-1 in the case of the Barbero-Immirzi parameter |γ| ≥ 1. PACS numbers: 04.60.Pp

Spin Foam Models for Quantum Gravity

2003

In the second part we concentrate on the definition of the Barrett-Crane model. We present the main results obtained in this framework from a critical perspective. Finally we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett-Crane model in this framework and review the finiteness results obtained for both its Riemannian as well as its Lorentzian variants.

Spin Foam Models of Quantum Gravity

Mathematical, Theoretical and Phenomenological Challenges Beyond the Standard Model - Perspectives of the Balkan Collaborations - BW2003 Workshop, 2005

We give a short review of the spin foam models of quantum gravity, with an emphasis on the Barret-Crane model. After explaining the shortcomings of the Barret-Crane model, we briefly discuss two new approaches, one based on the 3d spin foam state sum invariants for the embedded spin networks, and the other based on representing the string scattering amplitudes as 2d spin foam state sum invariants.

Canonical ``Loop'' Quantum Gravity and Spin Foam Models

1999

The canonical "loop" formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the theory are: 1) the complete calculation of the spectrum of geometric quantities like the area and the volume and the consequent physical predictions about the structure of the space-time at the Planck scale; 2) a microscopical derivation of the Bekenstein-Hawking black-hole entropy formula. Unfortunately, despite recent results, the dynamical aspect of the theory (imposition of the Wheller-De Witt constraint) remains elusive.

Spin foam model from canonical quantization

Physical Review D, 2008

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.

Construction of the general spin foam model of Lorentzian BF theory and gravity

In this article we report our progress in the construction of a general Lorentzian spin foam model based on the Gelfand-Naȋmark theory of the representations of SL(2, C). First we construct the simplex amplitude for the BF SL(2, C) model. Then we discuss the asymptotic limit of this model. Next we discuss the implemention of the Barrett-Crane constraints on this model. We derive an equation that the general Lorentzian spin foam model has to satisfy. In the appendix we give a simple derivation of the Clebsch-Gordan coefficients for SL(2, C). We have tried to make this article as much self contained as possible.