Results 1  10
of
11
Hamiltonian Analysis of nonchiral Plebanski Theory and its Generalizations
, 809
"... We consider nonchiral, full Lorentz groupbased Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with “internal” indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the l ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
(Show Context)
We consider nonchiral, full Lorentz groupbased Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with “internal” indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Φ carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Φ. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity, something that has not been appreciated in the literature treating them as being not much different from GR. 1
Spin Foams and Canonical Quantization
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2012
"... This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the threedimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemanni ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the threedimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev–Viro spin foam model, and how the Ponzano–Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the fourdimensional case, we recall a Lorentzcovariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Discrete Gravity Models and Loop Quantum Gravity: a Short Review
 SIGMA
, 2012
"... We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.
On the relations between gravity and BF theories
"... Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both selfdual and nonchiral formulations, their generalizations, and the MacDowell– Mansouri action.
Null twisted geometries
 Phys.Rev. D89 (2014) 084070 [1311.3279
"... We define and investigate a quantization of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrization of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantizatio ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We define and investigate a quantization of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrization of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with spacelike faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalism are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, Abelian geometric picture. It can be described by a Euclidean singular structure on the twodimensional spacelike surface defined by a foliation of spacetime by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper actionangle variables on the gaugeinvariant phase space are described by the eigenvectors of the Laplacian of the dual graph. We also identify the variables of the phase space amenable to characterize the extrinsic geometry of the foliation. Finally, we quantize the phase space and its algebra using Dirac’s algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labeled by SO(2) quantum numbers, and are embedded nontrivially in the unitary, infinitedimensional irreducible representations of the Lorentz group. 1