Polymer quantization of connection theories: Graph coherent states

Assanioussi, Mehdi

doi:10.1103/physrevd.98.045016

“…Moreover, the theoretical techniques used here can be further refined and generalized. Examples of these include using graph-coherent states [77] or stable coherent states [78]. Finally, one can hope that these insights into the cosmological model help to deal with the vast regularization ambiguities of the full theory.…”

Section: Discussionmentioning

confidence: 99%

New loop quantum cosmology modifications from gauge-covariant fluxes

Liegener

¹

,

Singh

²

2019

View full text Add to dashboard Cite

Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been succsessful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions build out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics of loop quantum cosmology is affected in a non-trivial way. The bounce turns out to be generically asymmetric with a rescaling of the Newton's constant in the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched resulting in an effective non-minimal coupling. These effects are shown to be common to different choices of regularization parameters.

show abstract

“…Our approach in the case of the interior region of a black hole is the same as the one adopted for flat homogeneous and isotropic cosmology [35,37]. Namely, the starting point is to consider a semi-classical coherent state on the Hilbert space of loop quantum gravity H, peaked on the classical configuration of interest (for more details on coherent states in LQG, see [44][45][46][47][48][49][50][51][52][53]). Then one computes the leading order, in a semi-classical expansion, of the expectation value of the LQG Hamiltonian operator originally proposed by Thiemann in its graph non-changing version [25,26,54,55] on the chosen semi-classical state.…”

Section: Effective Kantowski-sachs From Lqgmentioning

confidence: 99%

Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors

Assanioussi¹,

Dapor²,

Liegener³

2020

Self Cite

View full text Add to dashboard Cite

In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole, and develop a classical effective description for its interior which eventually resolves the singularity. However little progress has been made towards understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, from a calculation in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semi-classical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in General Relativity and the common effective Hamiltonian proposed in earlier literature.

show abstract

“…Let us notice that the valence N n of a node n can be written in the following form: N n = V n + 2L n , where V n is the valence of the node excluding loops and L n is the number of loops at the node n. As a result, the volume operator from (145) can be expressed by the number operator N n introduced in [38,39], which counts the number of loops at the node n. This observation can be used to study the coherence properties of the new graph coherent states with respect to the volume operator.…”

Section: Degeneracy Of the Eigenvalues Of The Volume Operatormentioning

confidence: 99%

Properties of the Rovelli–Smolin–DePietri volume operator in the spaces of monochromatic intertwiners

Kisielowski

¹

2021

Class. Quantum Grav.

View full text Add to dashboard Cite

We study some properties of the Rovelli–Smolin–DePietri volume operator in loop quantum gravity, which significantly simplify the diagonalization problem and shed some light on the pattern of degeneracy of the eigenstates. The operator is defined by its action in the spaces of tensor products H j 1 ⊗ ⋯ ⊗ H j N of the irreducible SU(2) representation spaces H j i , i = 1 , … , N , labelled with spins j i ∈ 1 2 N . We restrict to spaces of SU(2) invariant tensors (intertwiners) with all spins equal j 1 =⋯= j N = j. We call them spin j monochromatic intertwiners. Such spaces are important in the study of SU(2) gauge invariant states that are isotropic and can be applied to extract the cosmological sector of the theory. In the case of spin 1/2 we solve the eigenvalue problem completely: we show that the volume operator is proportional to identity and calculate the proportionality factor.

show abstract

Polymer quantization of connection theories: Graph coherent states

Cited by 6 publications

References 40 publications

New loop quantum cosmology modifications from gauge-covariant fluxes

New loop quantum cosmology modifications from gauge-covariant fluxes

Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors

Properties of the Rovelli–Smolin–DePietri volume operator in the spaces of monochromatic intertwiners

Contact Info

Product

Resources

About