Generalized spherically symmetric gravitational model: Hamiltonian dynamics in extended phase space and the BRST charge

Shestakova, T. P.

doi:10.1134/s020228931402011x

Cited by 6 publications

(5 citation statements)

References 26 publications

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“…we show that his assumption g 0a = 0, used to simplify his calculation of different contributions to the secondary constraints, is unwarranted; yet, remarkably his total Hamiltonian is equivalent to the one computed without the assumption g 0a = 0." Shestakova responded to the criticism by Kiriushcheva and her collaborators [49]. In the opinion of Natalia Kiriushcheva, the ADM approach already contains the loss of physics as this representation restricts possible coordinate transformations: a space-like hypersurface remains space-like.…”

Section: Appendix C: Setting Of Metric Terms Gµ0mentioning

confidence: 99%

Canonical reduction for dilatonic gravity in3+1dimensions

et al. 2016

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We generalize the 1 + 1-dimensional gravity formalism of Ohta and Mann to 3 + 1 dimensions by developing the canonical reduction of a proposed formalism applied to a system coupled with a set of point particles. This is done via the Arnowitt-Deser-Misner method and by eliminating the resulting constraints and imposing coordinate conditions. The reduced Hamiltonian is completely determined in terms of the particles' canonical variables (coordinates, dilaton field and momenta). It is found that the equation governing the dilaton field under suitable gauge and coordinate conditions, including the absence of transverse-traceless metric components, is a logarithmic Schrödinger equation. Thus, although different, the 3 + 1 formalism retains some essential features of the earlier 1 + 1 formalism, in particular the means of obtaining a quantum theory for dilatonic gravity.

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Section: Appendix C: Setting Of Metric Terms Gµ0mentioning

confidence: 99%

Canonical reduction for dilatonic gravity in3+1dimensions

et al. 2016

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“…Therefore, even though the variation of the gravitational Lagrangian will contribute to the total variation of the action, the additional terms will still take the form of some boundary contributions and the definition of the conserved charge can be given as in Eq.(33). A different apporach is discussed in [21], where it is chosen to work with a Lagrangian containing second-order derivatives such that the whole action is invariant and the conserved charge is simply the Noether one.…”

Section: Discussionmentioning

confidence: 99%

Dirac prescription from BRST symmetry in FRW space-time

Cianfrani

Montani

2013

Phys. Rev. D

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A procedure to define the BRST charge from the Noether one in extended phase space is given. It is outlined how this prescription can be applied to a Friedmann-Robertson-Walker space-time with a differential gauge condition and it allows us to reproduce the results of [20]. Then we discuss the cohomological classes associated with functions in extended phase space having ghost number one and we recover the frozen formalism for classical observables. Finally, we consider the quantization of BRST-closed states and we define a scalar product which implements the superHamiltonian constraint.

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“…and derive Hamiltonian equations in extended phase space. An explicit form of the Hamiltonian function, Lagrangian and Hamiltonian equations can be found in [9].…”

Section: S = Dtmentioning

confidence: 99%

Hamiltonian Dynamics in Extended Phase Space for Gravity and Its Consistency With Lagrangian Formalism: A Generalized Spherically Symmetric Model as an Example

Shestakova¹

2015

The Thirteenth Marcel Grossmann Meeting

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Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system with constraints. At the same time there exists another way to formulate Hamiltonian dynamics for constrained systems guided by the idea of extended phase space. We have already considered some features of this approach in the previous MG12 Meeting by the example of a simple isotropic model. Now we apply the approach to a generalized spherically symmetric model which imitates the structure of General Relativity much better. In particular, making use of a global BRST symmetry and the Noether theorem, we construct the BRST charge that generates correct gauge transformations for all gravitational degrees of freedom.As a rule, Hamiltonian formulation for gravity is constructed following to the Dirac scheme [1,2] and is a starting point for most attempts to quantize gravity. However, there are some reasons to doubt that Dirac Hamiltonian formulation for gravitational theory [3] can be thought as an equivalent one to the original General Relativity. Indeed, in Einstein formulation of General Relativity g 0µ components of metric tensor (µ = 0, 1, 2, 3) are treated on an equal basis with the rest of components, g ij (i, j = 1, 2, 3). The theory is invariant under gauge transformations that touch all metric components. In the Dirac approach only g ij components with their conjugate momenta are included into phase space, the transformations for this variables are generated by constraints. In fact, the original General Relativity and the Dirac formulation are theories with different groups of transformations. We can think of it as a considerable mathematical indication that Lagrangian and Hamiltonian formalism appear to be non-equivalent for the full theory of gravity. Moreover, the algebra of constraints in Dirac phase space does depend on parametrization of gravitational variables. It creates a serious obstacle to find an algorithm to construct a generator that would give correct transformations for all gravitational variables in 1

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Generalized spherically symmetric gravitational model: Hamiltonian dynamics in extended phase space and the BRST charge

Cited by 6 publications

References 26 publications

Canonical reduction for dilatonic gravity in3+1dimensions

Canonical reduction for dilatonic gravity in3+1dimensions

Dirac prescription from BRST symmetry in FRW space-time

Hamiltonian Dynamics in Extended Phase Space for Gravity and Its Consistency With Lagrangian Formalism: A Generalized Spherically Symmetric Model as an Example

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