Hamiltonian analysis of Plebanski theory

Buffenoir, Eric; Henneaux, Marc; Noui, Karim; Roche, Ph.

doi:10.1088/0264-9381/21/22/012

Cited by 90 publications

(240 citation statements)

References 32 publications

Supporting

Mentioning

237

Contrasting

Order By: Relevance

“…The term C(B) includes polynomial constraints, reducing topological BF to GR. 5 Typically, it gives the set of second class constraints expressing B in terms of the tetrad field (or vierbein) and leading to GR in the first order formalism (for a detailed canonical analysis of (43), see [17]). The BF theory can be quantized as described in Section 2, discretizing the spacetime manifold with a Regge triangulation (or more generally a cellular decomposition), and then evaluating the partition function (2), where the variables are the representations j t and intertwiners i τ .…”

Section: Towards the Quantum Gravity Amplitudementioning

confidence: 99%

New spinfoam vertex for quantum gravity

2007

View full text Add to dashboard Cite

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.

show abstract

Section: Towards the Quantum Gravity Amplitudementioning

confidence: 99%

New spinfoam vertex for quantum gravity

2007

View full text Add to dashboard Cite

show abstract

“…It is based on a passive interpretation where the (diffeomorphism) gauge transformations do not change the discretization, but rather values of the fields. Explicit calculations in the case of gravity, however, so far look complicated and we will not pursue a calculation of the amplitudes here [22]. Nevertheless, one can hope that at least their asymptotic behavior for large labels can be found easily, which would allow us to see whether or not the state sum will be finite.…”

Section: Spin Foam Measurementioning

confidence: 99%

Spin foam quantization and anomalies

Bojowald

Pérez

2009

Gen Relativ Gravit

View full text Add to dashboard Cite

Abstract. The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain-Kuchař model.

show abstract

“…This inclusion made sure that the path integral qualified as a reduced phase space quantisation of the theory, as it has been stressed in [95]. A similar analysis has been carried out for the Plebanski theory in [96], however, the resulting measure factor is widely ignored in the SFM literature. The result of the Gaussian integral is an interesting determinant that displays the full non linearity of Einstein's theory.…”

Section: The Holst Spin Foam Model Via Cubulationsmentioning

confidence: 88%

“…As it was shown in [96], if such constraints are taken into account, the measure present in the partition function should be augmented with a Jacobian coming from the Dirac brackets of the second class constraints.…”

Section: Spin Foam Models Through Bf Theorymentioning

confidence: 99%

Approaches to Quantum Gravity

Oriti

2009

215

View full text Add to dashboard Cite

One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed.In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of 'space' and 'time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other.This thesis is divided in two parts: in the first part we analyse LQG, paying particular attention to the semiclassical properties of the volume operator. Such an operator plays a pivotal role in defining the dynamics of the theory, thus testing its semiclassical limit is of uttermost importance. We then proceed to analyse spin foam models (SFM), which are an attempt at a covariant or path integral formulation of canonical Loop Quantum Gravity (LQG). In particular, in this thesis we propose a new SFM, whose path integral is defined in terms of the Holst action rather than the Plebanski action (used in current SFM). This departure from current SFM has enabled us to solve, explicitly, certain constraints which seem rather problematic in the current SFM.In the second part of this thesis we introduce Topos theory and how it has been utilised to reformulate quantum theory in a way that a consistent quantum logic can be defined. Moreover, we also define a Topos formulation of history quantum theory. The striking difference of this approach and the current consistent-history approach is that, in the former no fundamental role is played by the notion of a consistent sets (set of histories which do not interfere with each other) while, in the latter, such notions are central. This is an exciting departure since one of the main difficulty in the consistenthistory approach is how to choose the correct consistent set of history propositions, since there are many sets, most of which incompatible. However, we have s...

show abstract

Hamiltonian analysis of Plebanski theory

Cited by 90 publications

References 32 publications

New spinfoam vertex for quantum gravity

New spinfoam vertex for quantum gravity

Spin foam quantization and anomalies

Approaches to Quantum Gravity

Contact Info

Product

Resources

About