Canonical Commutation Relation Derived from Witt Algebra

Huber Nieto-Chaupis ()
Additional contact information
Huber Nieto-Chaupis: Faculty of Engineering, Universidad Autónoma del Perú, Lima 15842, Peru

Mathematics, 2025, vol. 13, issue 12, 1-16

Abstract: From an arbitrary definition of operators inspired by oscillators of Virasoro, an algebra is derived. It fits the structure of Virasoro algebra with null central charge or Witt algebra. The resulting formalism has yielded commutators with a dependence on integer numbers, and it follows the Witt-like algebra. Also, the quantum mechanics evolution operator for the case of the quantum harmonic oscillator was identified. Furthermore, the Schrödinger equation was systematically derived under the present framework. When operators are expressed in the framework of Hilbert space states, the resulting Witt algebra seems to be proportional to the well-known canonical commutation relation. This has demanded the development of a formalism based on arbitrary and physical operators as well as well-defined rules of commutation. The Witt-like was also redefined through the direct usage of the uncertainty principle. The results of the paper might suggest that Witt algebra encloses not only quantum mechanics’ fundamental commutator but also other unexplored relations among quantum mechanics observables and Witt algebra.

Keywords: Witt algebra; Virasoro algebra; quantum mechanics; commutators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/12/1910/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/12/1910/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:12:p:1910-:d:1674061

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().