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Eisenhart lift of Koopman-von Neumann mechanics. / Sen, Abhijit; Parida, Bikram Keshari; Dhasmana, Shailesh et al.

In: Journal of Geometry and Physics, Vol. 185, 104732, 03.2023.

Research output: Contribution to journal › Article › peer-review

Harvard

Sen, A, Parida, BK, Dhasmana, S & Silagadze, ZK 2023, 'Eisenhart lift of Koopman-von Neumann mechanics', Journal of Geometry and Physics, vol. 185, 104732. https://doi.org/10.1016/j.geomphys.2022.104732

APA

Sen, A., Parida, B. K., Dhasmana, S., & Silagadze, Z. K. (2023). Eisenhart lift of Koopman-von Neumann mechanics. Journal of Geometry and Physics, 185, [104732]. https://doi.org/10.1016/j.geomphys.2022.104732

Vancouver

Sen A, Parida BK, Dhasmana S, Silagadze ZK. Eisenhart lift of Koopman-von Neumann mechanics. Journal of Geometry and Physics. 2023 Mar;185:104732. doi: 10.1016/j.geomphys.2022.104732

Author

Sen, Abhijit ; Parida, Bikram Keshari ; Dhasmana, Shailesh et al. / Eisenhart lift of Koopman-von Neumann mechanics. In: Journal of Geometry and Physics. 2023 ; Vol. 185.

BibTeX

@article{9051572b45724b74b5c66d81d11dbf60,
title = "Eisenhart lift of Koopman-von Neumann mechanics",
abstract = "The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the fact that there is a Hilbert space representation of classical mechanics (also called Koopman-von Neumann mechanics) that attempts to give classical mechanics the same mathematical structure that quantum mechanics has. In this article, we geometrize the Koopman-von Newmann (KvN) mechanics using the Eisenhart toolkit. We then use a geometric view of KvN mechanics to find transformations that relate the harmonic oscillator, linear potential, and free particle in the context of KvN mechanics.",
keywords = "Classical mechanics, Eisenhart lift, Equivalence principle, Harmonic oscillator, Quantum mechanics",
author = "Abhijit Sen and Parida, {Bikram Keshari} and Shailesh Dhasmana and Silagadze, {Zurab K.}",
note = "The authors would like to thank Peter Horvathy and Anton Galajinsky for useful comments. The work of Z.K.S is supported by the Ministry of Education and Science of the Russian Federation.",
year = "2023",
month = mar,
doi = "10.1016/j.geomphys.2022.104732",
language = "English",
volume = "185",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Eisenhart lift of Koopman-von Neumann mechanics

AU - Sen, Abhijit

AU - Parida, Bikram Keshari

AU - Dhasmana, Shailesh

AU - Silagadze, Zurab K.

N1 - The authors would like to thank Peter Horvathy and Anton Galajinsky for useful comments. The work of Z.K.S is supported by the Ministry of Education and Science of the Russian Federation.

PY - 2023/3

Y1 - 2023/3

N2 - The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the fact that there is a Hilbert space representation of classical mechanics (also called Koopman-von Neumann mechanics) that attempts to give classical mechanics the same mathematical structure that quantum mechanics has. In this article, we geometrize the Koopman-von Newmann (KvN) mechanics using the Eisenhart toolkit. We then use a geometric view of KvN mechanics to find transformations that relate the harmonic oscillator, linear potential, and free particle in the context of KvN mechanics.

AB - The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the fact that there is a Hilbert space representation of classical mechanics (also called Koopman-von Neumann mechanics) that attempts to give classical mechanics the same mathematical structure that quantum mechanics has. In this article, we geometrize the Koopman-von Newmann (KvN) mechanics using the Eisenhart toolkit. We then use a geometric view of KvN mechanics to find transformations that relate the harmonic oscillator, linear potential, and free particle in the context of KvN mechanics.

KW - Classical mechanics

KW - Eisenhart lift

KW - Equivalence principle

KW - Harmonic oscillator

KW - Quantum mechanics

UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85145270200&partnerID=40&md5=af008dc06acc0eb8cc00095e19cacd63

UR - https://elibrary.ru/item.asp?id=50369224

UR - https://www.mendeley.com/catalogue/51bbe55e-254a-3e0a-abab-7019dd9a7752/

U2 - 10.1016/j.geomphys.2022.104732

DO - 10.1016/j.geomphys.2022.104732

M3 - Article

VL - 185

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

M1 - 104732

ER -

ID: 48699351