Eisenhart-Duval lift for minisuperspace quantum cosmology

Kan, Nahomi; Aoyama, Takuma; Hasegawa, Taiga; Shiraishi, Kiyoshi

doi:10.1103/physrevd.104.086001

Cited by 13 publications

(18 citation statements)

References 73 publications

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“…We will be following the Eisenhart-Duval lifting scheme [3,4] adjusted to the cosmological setup based on the scalartensor gravity [1,2]. In this method the minisuperspace associated with considered model is extended by introducing additional dynamical variable which makes possible to describe the evolution of the system in purely geometrical terms even in the presence of the potential.…”

Section: The Non-minimally Coupled Varying C and G Cosmological Modelmentioning

confidence: 99%

“…where x 3 parametrizes an additional degree of freedom of the extended minisuperpace. The metric of the extended minisuperspace (the lifted metric) is then given by [1]:…”

Section: The Non-minimally Coupled Varying C and G Cosmological Modelmentioning

confidence: 99%

“…In [1,2], it was shown that the extension of minisuperspace using the Eisenhart-Duval lift [3,4] provides a natural framework for introducing a Dirac-type equation. This equation can replace the Wheeler-DeWitt equation, which, as a hyperbolic partial differential equation, does not necessarily provide a positively defined probability density.…”

Section: Introductionmentioning

confidence: 99%

“…In such an extended minisuperspace, the dynamics of the system, which generally is not a geodesic one in the presence of the potential term, can be transformed into a geodesic dynamics associated with the socalled lifted metric that is suitably defined on the extended minisuperspace, since the "extended" equation of motion is expressed by the Laplace-Beltrami operator and thus exhibits covariance. Moreover, in [1,2] it was argued that the requirement of the covariance in the extended minisuperspace resolves the problem of factor ordering and may provide a consistent way to formulate the Dirac square root.…”

Section: Introductionmentioning

confidence: 99%

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Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

Balcerzak¹,

Lisaj²

2023

Preprint

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In this paper, we introduce a non-minimally coupled varying speed of light and varying gravitational constant cosmological toy model. Using the Eisenhart-Duval lifting method, we extend the original minisuperspace of the model and depict the evolution of the system in the presence of the potential term as a geometrical flow associated with the lifted metric. We write the Dirac-Wheeler-DeWitt equation, which solution is a spinor wave function of the Universe. Then we find the solution of the Dirac-Wheeler-DeWitt equation, which describes the emergence of two early universe-antiuniverse pairs that differ with the conserved quantity, which is an analog of the spin.

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Section: The Non-minimally Coupled Varying C and G Cosmological Modelmentioning

confidence: 99%

“…where x 3 parametrizes an additional degree of freedom of the extended minisuperpace. The metric of the extended minisuperspace (the lifted metric) is then given by [1]:…”

Section: The Non-minimally Coupled Varying C and G Cosmological Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

Balcerzak¹,

Lisaj²

2023

Preprint

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show abstract

“…First, lattice field theories are usually expressed in the Lagrangian formulation, and one needs to derive and optimize the corresponding Hamiltonian formulation (see, e.g., Refs. [128][129][130][131]). Second, one needs to match the different bare parameters and observables between these two formulations (see, e.g., Refs.…”

Section: Pos(lattice2022)228mentioning

confidence: 99%

Review on Quantum Computing for Lattice Field Theory

Funcke¹,

Hartung²,

Jansen³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

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Linearization of Newton’s Second Law

Paliathanasis

2024

Int J Theor Phys

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Eisenhart-Duval lift for minisuperspace quantum cosmology

Cited by 13 publications

References 73 publications

Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

Review on Quantum Computing for Lattice Field Theory

Linearization of Newton’s Second Law

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