Journal of Nonlinear Mathematical Physics

Volume 16, Issue 4, March 2013, 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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 4
Pages
421 - 430
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000455How to use a DOI?
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
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  - https://doi.org/10.1142/S1402925109000455
ID  - Pucacco2021
ER  -