Path integral renormalization in loop quantum cosmology

Bodendorfer, Norbert; Han, Muxin; Haneder, Fabian; Liu, Hongguang

doi:10.1103/physrevd.103.126021

Cited by 7 publications

(2 citation statements)

References 45 publications

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“…The method presented in this paper can be applied to spinfoam models with Lorentzian or Euclidean signatures and to compute bulk observables. An interesting perspective would be to compare the results obtained in the spinfoam-like path integral expansion formalism [61] with the ones in the full spinfoam one. This would give interesting insights into the canonicalcovariant relation.…”

Section: Discussionmentioning

confidence: 99%

Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology

Frisoni

Vidotto

Gozzini

2023

Class. Quantum Grav.

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We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph reﬁnement going from ﬁve to twenty boundary tetrahedra. This can be interpreted as a wave function of the universe, for which we compute boundary geometrical operators, correlation functions and entanglement entropy. The numerical calculation is made possible by adapting the Metropolis-Hastings algorithm, along with recently developed computational methods appropriate for the deep quantum regime. We conﬁrm that the transition amplitudes are stable against such reﬁnement. We ﬁnd that the average boundary geometry does not change, but the new degrees of freedom correct the quantum ﬂuctuations of the boundary and the correlations between spatial patches. The expectation values are compatible with their geometrical interpretation and the correlations between neighbouring patches decay when computed across diﬀerent spinfoam vertices.

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Section: Discussionmentioning

confidence: 99%

Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology

Frisoni

Vidotto

Gozzini

2023

Class. Quantum Grav.

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“…We already have at our disposal an operator whose eigenvalues are discrete, and with a superselected sector, it is the rotation generator J z , the idea is then to take the regularized metric coefficient to be [69]…”

Section: Singularity and Regularizationmentioning

confidence: 99%

Group quantization of the black hole minisuperspace

Sartini

2021

Preprint

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The emergence of non trivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess non null charges and hence map physical solutions to different ones. The symmetry group is isomorphic to the finite dimensional Poincaré group ISO(2, 1), whose irreducible representations are well known. This structure is used to build a consistent quantum theory of black hole minisuperspace. This has, among others, the striking consequence of implying a continuous spectrum for the mass operator.Following loop quantum cosmology, we obtain a regularization scheme compatible with the symmetry structure. It is possible to study the evolution of coherent states following the classical trajectories in the low curvature regime. We show that this produces an effective metric where the singularity is replaced by a Killing horizon merging two asymptotically flat regions. The quantum correction comes from a fundamental discreteness of spacetime, and the uncertainty on the energy of the system. Remarkably the effective evolution of semiclassical states is described by an effective Hamiltonian, related to the original one through a canonical transformation.

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On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

Mele,

Münch

2024

Class. Quantum Grav.

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In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume $V_o$, known as the \emph{fiducial cell}. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of $V_o$ is in turn essential for assessing the minisuperspace description's validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous minisuperspaces within the canonical framework and apply it to a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory's canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogenenity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on $V_o$. We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different $V_o$, and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ``first reduced, then quantised" approach can be reproduced is identified and the conditions for this to be a good approximation are determined.

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Path integral renormalization in loop quantum cosmology

Cited by 7 publications

References 45 publications

Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology

Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology

Group quantization of the black hole minisuperspace

On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

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