Volume 16, Issue 4, December 2009, Pages 421 - 430
Nonstandard Separability on the Minkowski Plane
Authors
Giuseppe Pucacco
Dipartimento di Fisica – Università di Roma “Tor Vergata”, INFN – Sezione di Roma II, Italy,pucacco@roma2.infn.it
Kjell Rosquist
Department of Physics, Stockholm University, 106 91 Stockholm, Sweden
ICRANet, Piazzale della Repubblica, 10, 65100 Pescara, Italy,kr@physto.se
Received 3 December 2008, Accepted 8 June 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925109000455How to use a DOI?
- Keywords
- Integrable Hamiltonian systems; separability by quadrature
- Abstract
We present examples of nonstandard separation of the natural Hamilton–Jacobi equation on the Minkowski plane 𝕄2. By “nonstandard” we refer to the cases in which the form of the metric, when expressed in separating coordinates, does not have the usual Liouville structure. There are two possibilities: the “complex-Liouville” (or “harmonic”) case and the “linear/null” (or “Jordan block”) case. By means of explicit examples, we show that, in all cases, a suitable glueing of coordinate patches of the different structures allows us to separate natural systems with indefinite kinetic energy all over 𝕄2.
- Copyright
- © 2009 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/).
Cite this article
TY - JOUR AU - Giuseppe Pucacco AU - Kjell Rosquist PY - 2021 DA - 2021/01/07 TI - Nonstandard Separability on the Minkowski Plane JO - Journal of Nonlinear Mathematical Physics SP - 421 EP - 430 VL - 16 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000455 DO - 10.1142/S1402925109000455 ID - Pucacco2021 ER -