Canonical analysis with no second-class constraints of 
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 gravity with Immirzi parameter

Montesinos, Merced; Celada, Mariano

doi:10.1103/physrevd.101.084043

Cited by 6 publications

(9 citation statements)

References 28 publications

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“…When analyzing the ECH Lagrangian without the time gauge, complications arise due to the presence of second class constraints, 8 which are precisely the primary simplicity constraints and their conjugated secondary constraints [63,84,87]. These can be dealt with either by using the Dirac bracket [85,86], by working with an explicit solution of the constraints [88][89][90][134][135][136][137], or by adding variables to promote the constraints to a first class set (so-called gauge unfixing) [110,111,138]. In all cases, one arrives at the conclusion that the choice of Lorentz connection configuration variable is ambiguous in the bulk [63,91], an observation which has fueled the discussion on the ambiguities of the imposition of the spin foam simplicity constraints.…”

Section: A New Look At Canonical Analysismentioning

confidence: 99%

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Freidel

Geiller

Pranzetti

2020

J. High Energ. Phys.

118

195

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In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local $$ \mathfrak{sl} $$ sl (2, ℂ) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local $$ \mathfrak{sl} $$ sl (2, ℝ) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.

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Section: A New Look At Canonical Analysismentioning

confidence: 99%

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Freidel

Geiller

Pranzetti

2020

J. High Energ. Phys.

118

195

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“…In this paper we show that the strategy of Ref. [9] can also be applied to general relativity in n dimensions expressed as a constrained BF theory. Consequently, this work extends to higher dimensions the results of Ref.…”

Section: Introductionmentioning

confidence: 90%

“…In such a Hamiltonian formulation the solution of the Plebanski 2-forms in terms of the tetrads is never used; it is not needed. More recently, a similar strategy was used to get the Hamiltonian formulation of BF gravity involving the Immirzi parameter (and the cosmological constant) [9]. Nevertheless, in the latter case, it is not enough to solve the constraint on the B fields as in the Plebanski action because by doing so it leads to a form of the action involving a presymplectic structure, which needs to be further reduced by doing a suitable parametrization of the connection in terms of the final configuration variable and some auxiliary fields.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, in the latter case, it is not enough to solve the constraint on the B fields as in the Plebanski action because by doing so it leads to a form of the action involving a presymplectic structure, which needs to be further reduced by doing a suitable parametrization of the connection in terms of the final configuration variable and some auxiliary fields. After integrating out the auxiliary fields the Hamiltonian formulation involving only first-class constraints is achieved [9]. One relevant aspect of such a Hamiltonian formulation is that the tetrad is never used.…”

Section: Introductionmentioning

confidence: 99%

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Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions

Montesinos,

Escobedo,

Celada

2021

Preprint

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We perform, in a manifestly SO(n − 1, 1) [SO(n)] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions written as a constrained BF theory. We solve the constraint on the B field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.

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“…[10,11] for a derivation with second-class constraints). The same formulation was also obtained from the canonical analysis of BF gravity with the Immirzi parameter while again avoiding the presence of second-class constraints [12], thus simplifying previous analyses (see for instance Ref. [13]).…”

Section: Introductionmentioning

confidence: 99%

Canonical analysis of $BF$ gravity in $n$ dimensions

Celada¹,

Escobedo²,

Montesinos³

2020

Preprint

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In this paper we perform in a manifestly SO(n − 1, 1) [or, alternatively SO(n)] covariant fashion, the canonical analysis of general relativity in n dimensions written as a constrained BF theory. Since the Lagrangian action of the theory can be written in two classically equivalent ways, we analyze each case separately. We show that for either action the canonical analysis can be accomplished without introducing second-class constraints during the whole process. Furthermore, in each case the resulting Hamiltonian formulation is the same as the canonical formulation with only first-class constraints recently obtained in Ref.[1] from the n-dimensional Palatini action.

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Canonical analysis with no second-class constraints of BF gravity with Immirzi parameter

Cited by 6 publications

References 28 publications

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions

Canonical analysis of $BF$ gravity in $n$ dimensions

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