The Superspace of geometrodynamics

Giulini, Domenico

doi:10.1007/s10714-009-0771-4

Cited by 55 publications

(71 citation statements)

References 71 publications

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“…A central conceptual issue in drawing this analogy is the adaptation of the very notion of a hydrodynamic interpretation to the background-independent context: we cannot expect to obtain a description in terms of a 'fluid' on spacetime; instead a field capturing some effective degrees of freedom of quantum geometry is defined on the configuration space for gravity, i.e. superspace, the space of geometries [19]. A natural possibility is to view the collective wavefunction appearing in the definition of a condensate state as a wavefunctionà la Wheeler-DeWitt quantum cosmology.…”

Section: Jhep06(2014)013mentioning

confidence: 99%

“…Information about the connection can be extracted from expectation values of suitable operators, for instance 19) where χ can be seen as a character of a suitable product of group elements. In the case of G = SU(2), for instance, taking χ to be the trace in the j = ) give a complete set of functions on SU(2) 4 that are invariant under g I → g I k and g I → k ′ g I , which motivates their identification with components of the curvature for a single tetrahedron.…”

Section: Jhep06(2014)013mentioning

confidence: 99%

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Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

136

256

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We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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Section: Jhep06(2014)013mentioning

confidence: 99%

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

136

256

View full text Add to dashboard Cite

show abstract

“…Scalar constraint determines dynamics, vector one merely reflects diffeoinvariance. Making use of the conjugate momenta, first formula in (12), and the scalar constraint transforms into the Hamilton-Jacobi type equation (13) is the DeWitt metric on the Wheeler super space, a factor space of all ∞ c Riemannia metrics on ∂M , and a group of all ∞ c diffeomorphisms of ∂M that preserve orientation [29][30][31]. The Dirac-Faddeev primary canonical quantization method [28,32] in the present case has the form …”

Section: Standard Quantum Geometrodynamicsmentioning

confidence: 99%

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Glinka¹

2014

J Astrophys Aerospace Technol

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The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global onedimensionality conjecture within quantum general relativity, first considered by the author in 2010 and then in 2012. In this model the global dimension is a determinant of a metric of three-dimensional space embedded into an enveloping Lorentizan four-dimensional space-time. In 2012, it has already been presented by the author that this model can be extended to any Lorentzian D + 1-dimensional space-time, where D is a dimension of space, and resulting in the global one-dimensional model of a higher dimensional quantum gravity.The purely quantum-mechanical part of this model is a minimal effective model within the quantum Geometrodynamics, introduced by J.A. Wheeler and B.S. DeWitt in the 1960s, but the effective potential is manifestly different from the one considered by Wheeler & DeWitt. Moreover, in our model the wave functionals solving the quantum gravity are one-variable smooth functions and, therefore, the troublesome mathematical technique of the Feynman functional integration present in the Hawking formulation of quantum gravity, is absent is this model, what makes it a mathematically consistent theory of quantum gravitation.In this paper, we discuss in some detail a certain part of the global one-dimensional model already proposed in 2010, and then developed in 2012. The generalized functional expansion of the effective potential and the residual approximation, which describe the embedded spaces which are maximally symmetric three-dimensional Einstein's manifolds, whose lead to the Newton-Coulomb type potential in the quantum gravity model, are considered. Furthermore, scenarios related to few selected specific forms of the effective potential are suggested as physically interesting and discussed.

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“…Since we have from above that Dif f (σ) is implemented on phase space by the action of the momentum constraints we know that precisely the reduced space we are looking for can be achieved by quotienting out the gauge orbits associated with those constraints according to the symplectic reduction procedure above. This, in fact, leads us directly to Wheeler's superspace (see Wheeler (1968), Giulini (2009)) upon which a formulation of canonical general relativity would be constituted according to this brand of spatial reductive relationalism. With regard to time things are, as ever, far more complicated.…”

Section: Reductive Spacetime Relationalismmentioning

confidence: 99%

Three denials of time in the interpretation of canonical gravity

Thébault¹

2012

Studies in History and Philosophy of Science Part B: Studies in

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The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constrains in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of a hypersurface embedded within a solution. A first denial of time in the context of a position of reductive temporal relationalism can be shown to be troubled by failure on the first count, and second denial in the context Machian temporal relationalism can be found to be hampered by failure on the second. A third denial of time, consistent with both the of the Hamiltonian constraints roles, is constituted by the implementation of a scheme for constructing observables in terms of correlations. The motivation for and implications of each of these three denials are investigated.

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The Superspace of geometrodynamics

Abstract: Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.

Cited by 55 publications

References 71 publications

Homogeneous cosmologies as group field theory condensates

Homogeneous cosmologies as group field theory condensates

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Three denials of time in the interpretation of canonical gravity

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