119087029
Dirac and Lagrangian reductions in the canonical approach to the first-order form of the Einstein–Hilbert action
Abstract It is shown that the Lagrangian reduction, in which solutions of equations of motion that do not involve time derivatives are used to eliminate variables, leads to results quite different from the standard Dirac treatment of the first-order form of the Einstein–Hilbert action when the equations of motion correspond to the first class constraints. A form of the first-order formulation of the Einstein–Hilbert action which is more suitable for the Dirac approach to constrained systems is presented. The Dirac and reduced approaches are compared and contrasted. This general discussion is illustrated by a simple model in which all constraints and the gauge transformations which correspond to first class constraints are completely worked out using both methods to demonstrate explicitly their differences. These results show an inconsistency in the previous treatment of the first-order Einstein–Hilbert action which is likely responsible for problems with its canonical quantization.
119248889
Analysis of the Hamiltonian formulations of linearized general relativity
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-2 theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant modifications to the initial covariant Lagrangian (similar to those modifications used in full gravity) are in fact unnecessary. The Hamiltonians and the constraints are different in these two formulations but the structure of the constraint algebra and the gauge invariance derived from it are the same. It is shown that these equivalent Hamiltonian formulations are related to each other by a canonical transformation, which is explicitly given. The relevance of these results to the full theory of General Relativity is briefly discussed.
117314216
Comment on `Hamiltonian formulation for the theory of gravity and canonical transformations in extended phase space' by T P Shestakova
We argue that the conclusion, `we cannot consider the Dirac approach as fundamental and undoubted', made in the paper by Shestakova (Class. Quantum Grav. 28 055009, 2011), is based upon an incomplete and flawed analysis of the simple model presented in section 3 of the article. We re-examine the analysis of this model and find that it does not support the author's conclusion. For the theory of gravity neither the equivalence of the effective action nor its Hamiltonian formulation is given by the author, therefore, we only provide a brief commentary.
119222199
The Hamiltonian formulation of tetrad gravity: Three-dimensional case
The Hamiltonian formulation of tetrad gravity in any dimension higher than two, using its first-order form where tetrads and spin connections are treated as independent variables, is discussed, and the complete solution of the three-dimensional case is given. For the first time, applying the methods of constrained dynamics, the Hamiltonian and constraints are explicitly derived and the algebra of Poisson brackets among all constraints is calculated. The algebra of Poisson brackets, among first-class secondary constraints, locally coincides with Lie algebra of the ISO(2,1) Poincaré group. All the first-class constraints of this formulation, according to the Dirac conjecture and using the Castellani procedure, allow us to unambiguously derive the generator of gauge transformations and find the gauge transformations of the tetrads and spin connections which turn out to be the same as found by Witten without recourse to the Hamiltonian methods [Nucl. Phys. B 311, 46 (1988)]. The gauge symmetry of the tetrad gravity generated by the Lie algebra of constraints is compared with another invariance, diffeomorphism. Some conclusions about the Hamiltonian formulation in higher dimensions are briefly discussed; in particular, that diffeomorphism invariance is not derivable as a gauge symmetry from the Hamiltonian formulation of tetrad gravity in any dimension where tetrads and spin connections are used as independent variables.
119213240
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
Abstract It is shown that when the Einstein–Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity.
122626470
Remarks on 'Note about Hamiltonian formalism of healthy extended Horava-Lifshitz gravity' by J. Kluson
We reassess the conclusion by Klusoyn (J. High Energy Phys. 1007 (2010) 038) that the Hamiltonian formulation of the healthy extended Hoyrava-Lifshitz gravity does not present any problem.
100638900
On Separation of Gagolinium's Isotopes by Means of Isotopically Selective ICRH