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Volume 20, Issue 3, October 2013, Pages 451 - 463
Quantizing preserving Noether symmetries
Authors
M.C. Nucci
Dipartimento di Matematica e Informatica Università degli Studi di Perugia & INFN Sezione di Perugia
06123 Perugia, Italy,mariaclara.nucci@unipg.it
Received 27 January 2013, Accepted 11 September 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.855053How to use a DOI?
- Keywords
- Classical quantization; Lie symmetries; Noether symmetries; Calogero's goldfish many-body problem
- Abstract
A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. Two examples are given, one known and one new: the quantization of a charged particle in a uniform magnetic field in the plane, and that of the ‘goldfish’ many-body problem extensively studied by Calogero et al.
- Copyright
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - M.C. Nucci PY - 2021 DA - 2021/01/06 TI - Quantizing preserving Noether symmetries JO - Journal of Nonlinear Mathematical Physics SP - 451 EP - 463 VL - 20 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.855053 DO - 10.1080/14029251.2013.855053 ID - Nucci2021 ER -