Eisenhart-Duval lift for minisuperspace quantum cosmology

  title={Eisenhart-Duval lift for minisuperspace quantum cosmology},
  author={Nahomi Kan and Takuma Aoyama and Taiga Hasegawa and Kiyoshi Shiraishi},
  journal={Physical Review D},
Takuma Aoyama, Taiga Hasegawa, and Kiyoshi Shiraishi Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Yamaguchi-shi, Yamaguchi 753–8512, Japan (Dated: July 29, 2021) We study covariant equations in quantum cosmology of an extended minisuperspace obtained by the Eisenhart–Duval lift. We find that a Dirac-type equation is naturally introduced in the extended minisuperspace. Explicit forms of the fundamental solutions are yielded for specific models. The possible… 
1 Citations
Third quantization for scalar and spinor wave functions of the Universe in an extended minisuperspace
We consider the third quantization in quantum cosmology of a minisuperspace extended by the Eisenhart–Duval lift. We study the third quantization based on both Klein–Gordon type and Dirac-type


Remarks on Kantowski-Sachs quantum cosmology
Abstract The Kantowski-Sachs model is shown to be an important toy model in quantum cosmology due to its simplicity. This allows one to treat it in different ways although it is an anisotropic model
Supersymmetric quantum cosmology proposals and the Bianchi type-II model.
This hidden symmetry method is extended to the Bianchi type-II model finding the full expansion for Ψ, which contains terms satisfying the no-boundary proposal of Hartle and Hawking but also terms behaving as proposed by Hawking for quantum wormhole states.
Quantization of the Taub model with extrinsic time
The paper addresses the quantization of minisuperspace cosmological models, with application to the Taub Model. By desparametrizing the model with an extrinsic time, a formalism is developed in order
Cosmological aspects of the Eisenhart–Duval lift
A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed
Derivation of the Wheeler-DeWitt equation from a path integral for minisuperspace models.
  • Halliwell
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1988
The relationship between path-integral and Dirac quantization for a simple class of reparametrization-invariant theories and the results are applied to two simple examples: the nonrelativistic point particle in parametrized form and the relativity point particle.
Spectrum of wormholes.
  • Hawking, Page
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1990
Wormholes have been studied mainly in the semiclassical approximation as solutions of the classical Euclidean field equations, but one can represent wormholes in a more general manner as Solutions of the Wheeler-DeWitt equation with appropriate boundary conditions.
Dirac Decomposition of Wheeler-DeWitt Equation in the Bianchi Class A Models
The Wheeler-DeWitt equation in the Bianchi Class A cosmological models is expressed generally in terms of a second-order differential equation, like the Klein-Gordon equation. To obtain a positive
Wave packet in quantum cosmology.
  • Kazama, Nakayama
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1985
A simple Friedmann-Robertson- Walker-Walker-type minisuperspace model is proposed, in which issues (a)--(b) probability interpretation, and (c) the emergence of a classical universe in the quantum framework are successfully solved.
Quantization of minisuperspaces as ordinary gauge systems
Simple cosmological models are used to show that gravitation can be quantized as an ordinary gauge system if the Hamilton–Jacobi equation for the model under consideration is separable. In this
Supersymmetric Bianchi models and the square root of the Wheeler-DeWitt equation
Abstract By solving the full set of quantum constraint equations for the Bianchi-I mini-superspace model in supergravity, it is found that the wave-function depends only on two arbitrary constants.