Hamiltonian analysis of \mathsf {SO}(4,1) -constrained BF theory

Durka, Remigiusz; Kowalski-Glikman, Jerzy

doi:10.1088/0264-9381/27/18/185008

Cited by 14 publications

(13 citation statements)

References 30 publications

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“…14) which implies precisely equation(4.13).From equation (4.13) it follows that the BF vacuum polarisation vanishes and the Feynman propagators (2.12) coincide with the dressed propagators.…”

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confidence: 60%

Perturbative BF theory

Guadagnini

Rottoli

2020

Nuclear Physics B

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We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU (2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renomalization of this model defined in R 3 is presented. The structure of the ISU (2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalized traces of ISU (2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out. and S φπ can be written aswhere the bracket ·· JP denotes the non-degenerate bilinear form [9] on the ISU(2) algebra J a P b JP = δ ab , J a J b JP = 0 = P a P b JP .

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confidence: 60%

Perturbative BF theory

Guadagnini

Rottoli

2020

Nuclear Physics B

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“…This model has been already investigated by the author in the several different contexts, like canonical analysis [20], supergravity [21], and the AdS-Maxwell group of symmetries [22,23]. Additionally, the entropy of BF theory in the context of the entropic force was discussed in [24].…”

Section: From Macdowell-mansouri Gravity To Bf Theorymentioning

confidence: 99%

Immirzi parameter and Noether charges in first order gravity

Durka¹

2012

J. Phys.: Conf. Ser.

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The framework of SO(3, 2) constrained BF theory applied to gravity makes it possible to generalize formulas for gravitational diffeomorphic Noether charges (mass, angular momentum, and entropy). It extends Wald's approach to the case of first order gravity with a negative cosmological constant, the Holst modification and the topological terms (Nieh-Yan, Euler, and Pontryagin).Topological invariants play essential role contributing to the boundary terms in the regularization scheme for the asymptotically AdS spacetimes, so that the differentiability of the action is automatically secured. Intriguingly, it turns out that the black hole thermodynamics does not depend on the Immirzi parameter for the AdS-Schwarzschild, AdS-Kerr, and topological black holes, whereas a nontrivial modification appears for the AdS-Taub-NUT spacetime, where it impacts not only the entropy, but also the total mass.

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“…As we mentioned, the two-dimensional Polynomial BF action is closely related to the four-dimensional MacDowell-Mansouri Gravity, and our canonical analysis needs no gauge fixing condition at the classical level, in contrast with the analysis of the MacDowell-Mansouri BF theory shown in [29]. Therefore, our analysis can shed some light in the canonical analysis of the four dimensional BF theory using the Hamilton-Jacobi formalism [17], for example.…”

Section: Final Remarksmentioning

confidence: 90%

Constraint analysis of two-dimensional quadratic gravity from $${ BF}$$ B F theory

Valcárcel

2016

Gen Relativ Gravit

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Quadratic gravity in two dimensions can be formulated as a Background Field (BF ) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions.In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.

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Hamiltonian analysis of \mathsf {SO}(4,1) -constrained BF theory

Cited by 14 publications

References 30 publications

Perturbative BF theory

Perturbative BF theory

Immirzi parameter and Noether charges in first order gravity

Constraint analysis of two-dimensional quadratic gravity from $${ BF}$$ B F theory

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