Geometric aspects of quantization and relationship to integrability

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

11-2023

Abstract

It is the case that quantum mechanics has a deep geometric structure and can be presented accordingly. Quantum mechanics is to a certain degree foreshadowed by the geometry inherent in the geometric structure of classical mechanics. The purpose here is to present some new results and proofs which impact the mathematical structure of quantum mechanics. The relationship between integrability and quantum physics is investigated in terms of geometric ideas and structures. Two physical examples are drawn from these mathematical ideas which directly relate to physics. An introduction as to how these ideas can be extended to infinite degrees of freedom is also described.

Comments

© 2023 The Author(s).

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Recommended Citation

Bracken, Paul. "Geometric aspects of quantization and relationship to integrability." Physica Scripta 98, no. 12 (2023): 125202. https://doi.org/10.1088/1402-4896/ad052a

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Physica Scripta

DOI

10.1088/1402-4896/ad052a