Plebanski theory and covariant canonical formulation

Alexandrov, Sergei; Buffenoir, Eric; Roché, Philippe

doi:10.1088/0264-9381/24/11/003

Cited by 30 publications

(64 citation statements)

References 27 publications

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“…If such a relation exists, it should rely on a more sophisticated choice of reality conditions. Finally, we have also observed that there are sectors in phase space, characterized by vanishing of the two (partial Dirac) brackets (52), where this classification of constraints may fail, in particular, leading to fewer degrees of freedom. In fact, the existence of special sectors in phase space with a drastically different canonical structure is not an unusual situation.…”

Section: Discussionmentioning

confidence: 66%

Chiral description of massive gravity

Alexandrov

Krasnov

Speziale

2013

J. High Energ. Phys.

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We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure similar to that of SU(2) gauge theories. The chiral description simplifies computations of the constraint algebra, and allows us to perform the complete canonical analysis of the system. In particular, we explicitly compute the secondary constraint and carry out the stabilization procedure, thus proving that in general the theory propagates 7 degrees of freedom, consistently with previous claims. Finally, we point out that the description in terms of 2-forms opens the door to an infinite class of ghost-free massive bi-gravity actions. Our results apply directly to Euclidean signature. The reality conditions to be imposed in the Lorentzian signature appear to be more complicated than in the usual gravity case and are left as an open issue.

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Section: Discussionmentioning

confidence: 66%

Chiral description of massive gravity

Alexandrov

Krasnov

Speziale

2013

J. High Energ. Phys.

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“…In fact this choice is physically motivated as SU (2) is the gauge group if we want to include fermionic matter [272]. 14 In the physics of the standard model we are used to identifying the coordinate t with the physical time of a suitable family of observers. In the general covariant context of gravitational physics the coordinate time t plays the role of a label with no physical relevance.…”

Section: Canonical Analysismentioning

confidence: 99%

“…Alternatively, one can associate the boundary states with elements of L 2 (Spin(4) N ℓ ) (in the Riemannian models) -or carefully define the analog of spin network states as distributions in the Lorentzian case 25 . In this case one gets special kind of spin network states that are a subclass of the so-called projected spin networks introduced in [16,241] in order to define an heuristic quantization of the (non-commutative and very complicated) Dirac algebra of a Lorentz connection formulation of the phase space of gravity [14,10,16,9,8,7,15]. The fact that these special subclass of projected spin networks appear naturally as boundary states of the new spin foams is shown in [152].…”

Section: Boundary Data For the New Models And Relationship With The Cmentioning

confidence: 99%

The Spin-Foam Approach to Quantum Gravity

Pérez

2013

Living Rev. Relativ.

557

725

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This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.

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“…We will proceed in two steps, motivated by the structure of (15). First, we focus on a single link, studying the phase space T * SL(2, C) and the pair of simplicity constraints (14), which are local on the links.…”

Section: Simple Bivectors and Null Polyhedramentioning

confidence: 99%

“…Hence, the node algebra contains 2m − 1 first class constraints and two pairs of second class constraints. Using this result, and reintroducing the F 1 's (one independent first class constraint per link), the counting of dimensions of the reduced phase space S Γ defined in (15) gives…”

Section: Null Twisted Geometriesmentioning

confidence: 99%

Null twisted geometries

Speziale

Zhang

2014

Phys. Rev. D

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We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation 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 space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims 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 an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is naturally decomposed into a conformal metric and scale factors, forming locally conjugate pairs. Proper action-angle variables on the gauge-invariant 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 quantise the phase space and its algebra using Dirac's algorithm, obtaining a notion of spin networks for null hypersurfaces. Such spin networks are labelled by SO(2) quantum numbers, and are embedded non-trivially in the unitary, infinite-dimensional irreducible representations of the Lorentz group.Comment: 22 pages, 3 figures. v2: minor corrections, improved presentation in section 4, references update

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Plebanski theory and covariant canonical formulation

Cited by 30 publications

References 27 publications

Chiral description of massive gravity

Chiral description of massive gravity

The Spin-Foam Approach to Quantum Gravity

Null twisted geometries

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