ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra

Okołów, Andrzej

doi:10.1007/s10714-013-1636-4

Cited by 16 publications

(18 citation statements)

References 11 publications

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“…This will show under which circumstances the constraint algebra closes, and under which circumstances additional constraints must be included, and finally lead to the full, dynamical Hamiltonian. It should be noted that the calculation of the Poisson brackets is straightforward, although it can be very lengthy, even in the case of TEGR [11]. Naively, the unconstrained case would be the easiest, since it involves the least number of constraints to calculate Poisson brackets with.…”

Section: Discussionmentioning

confidence: 99%

“…However, for particular values of the parameters the terms which cause this behavior are absent from the action, thus allowing the Poisson brackets to close [25]. Due to the lengthiness of the calculations even in seemingly simple cases such as TEGR [11] we present these studies in separate articles. Another potential issue that must receive attention is the possible bifurcation of constraints, i.e., the situation where the closing or non-closing of the Poisson brackets depends on the particular values of the fields, as found in previous studies [32], which we plan to investigate in detail in further work.…”

Section: The Ngr Hamiltonianmentioning

confidence: 99%

“…This can be done best in terms of a full-fledged Hamiltonian analysis in terms of the Dirac-Bergmann algorithm for constrained Hamiltonian systems. It is known that the teleparallel equivalent of general relativity (TEGR), which yields the same dynamics and solutions for the metric defined by the tetrads as general relativity and contains no additional degrees of freedom, is self-consistent and ghost-free [10][11][12][13][14][15][16]. The hope is that this is not the only contender of the class of healthy teleparallel theories of gravity in this sense.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian and primary constraints of new general relativity

2019

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We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear. * blixt@ut.ee † manuel.hohmann@ut.ee ‡ christian.pfeifer@ut.ee

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Section: Discussionmentioning

confidence: 99%

Section: The Ngr Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hamiltonian and primary constraints of new general relativity

2019

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“…[10] that deals with an enlarged set of variables and constraints to enforce the vanishing of the curvature. The canonical formulation of TEGR has been also stated in the geometric language of differential forms [14,15].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian formulation of teleparallel gravity

2016

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The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.Comment: 13 pages, no figures, comments welcom

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“…Solutions of these equations play an important role in deriving an ADM-like Hamiltonian framework of TEGR [4,8] and YMTM [15]-the configuration variable of Lagrangian formulations of TEGR and YMTM is a cotetrad field on a four-dimensional manifold; the cotetrad field is decomposed into "time-like" and "space-like" parts the latter one being (θ A ) ∈ Θ; then a solution of (4.14) is used to express the "time-like" part as a function of the ADM lapse function, the ADM shift vector field and (θ A ). Moreover, a solution of (4.14) appears in formulae describing constraints of both TEGR and YMTM, and the equations (4.14) are used repeatedly while deriving constraint algebras of both theories [8,17,15]. Note that at every point y ∈ Σ the values (ξ A (y)) of a solution of (4.14) form a timelike vector in M which means that the value ξ 0 (y) cannot be 0.…”

Section: New Variables and New Dofmentioning

confidence: 99%

Variables suitable for constructing quantum states for the teleparallel equivalent of general relativity I

Okołów

2013

Gen Relativ Gravit

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We present the first part of an analysis aimed at introducing variables which are suitable for constructing a space of quantum states for the Teleparallel Equivalent of General Relativity via projective techniques-the space is meant to be applied in a canonical quantization of the theory. We show that natural configuration variables on the phase space of the theory can be used to construct a space of quantum states which however possesses an undesired property. We introduce then a family of new variables such that some elements of the family can be applied to build a space of quantum states free of that property. * This is an author-created version of a paper published as Gen. See [1] for the newest review on TEGR.These results mean that the eigenvalues of (q IJ ) are 1, 1 and

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ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra

Abstract: We derive a new constraint algebra for a Hamiltonian formulation of the Teleparallel Equivalent of General Relativity treated as a theory of cotetrad fields on a spacetime. The algebra turns out to be closed.

Cited by 16 publications

References 11 publications

Hamiltonian and primary constraints of new general relativity

Hamiltonian and primary constraints of new general relativity

Hamiltonian formulation of teleparallel gravity

Variables suitable for constructing quantum states for the teleparallel equivalent of general relativity I

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