TY - JOUR

T1 - Integrable minisuperspace models with Liouville field: energy density self-adjointness and semiclassical wave packets

AU - Андрианов, Александр Андреевич

AU - Лан, Чень

AU - Новиков, Олег Олегович

AU - Вонг, Йи-Фан

N1 - Funding Information: Acknowledgements The funding for this work was provided by the RFBR projects 16-02-00348 and 18-02-00264 (A. A. and O. N.) and the Spanish MINECO under project MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘Maria de Maeztu’), Grant FPA2016-76005-C2-1-P, Grant 2014-SGR-104 (Generalitat de Catalunya) (A. A.). Y. -F. Wang is grateful to the Bonn-Cologne Graduate School for Physics and Astronomy (BCGS) for financial support. The authors are grateful to Claus Kiefer for illuminating comments and suggestions as well as to Maxim Kurkov for valuable remarks. Y. -F. Wang is also grateful to Nick Kwidzinski, Dennis Piontek and Tim Schmitz for inspiring discussions.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum contexts of Wheeler–DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and phantom field, the energy density operators are not essentially self-adjoint, and self-adjoint extensions contain ambiguities. Therefore the same classical actions correspond to a family of distinct quantum models. For the phantom field the energy spectrum happens to be discrete. The probability conservation and appropriate classical limit can be achieved with a certain restriction of the functional class. The appropriately localized wave packets are studied numerically using the Schrödinger’s norm and a conserved Mostafazadeh’s norm introduced from techniques of pseudo-Hermitian quantum mechanics. These norms give a similar packet evolution that is confronted with analytical classical solutions.

AB - The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum contexts of Wheeler–DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and phantom field, the energy density operators are not essentially self-adjoint, and self-adjoint extensions contain ambiguities. Therefore the same classical actions correspond to a family of distinct quantum models. For the phantom field the energy spectrum happens to be discrete. The probability conservation and appropriate classical limit can be achieved with a certain restriction of the functional class. The appropriately localized wave packets are studied numerically using the Schrödinger’s norm and a conserved Mostafazadeh’s norm introduced from techniques of pseudo-Hermitian quantum mechanics. These norms give a similar packet evolution that is confronted with analytical classical solutions.

KW - BORN-OPPENHEIMER CONTEXT

KW - QUANTUM COSMOLOGY

KW - SCALAR FIELDS

KW - DARK ENERGY

KW - MECHANICS

KW - GRAVITY

KW - INFLATION

KW - COMPONENT

KW - OPERATORS

KW - SYMMETRY

UR - http://www.scopus.com/inward/record.url?scp=85053930579&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/integrable-minisuperspace-models-liouville-field-energy-density-selfadjointness-semiclassical-wave-p

U2 - 10.1140/epjc/s10052-018-6255-5

DO - 10.1140/epjc/s10052-018-6255-5

M3 - Article

VL - 78

JO - European Physical Journal C

JF - European Physical Journal C

SN - 1434-6044

IS - 9

M1 - 786

ER -