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Journal of Applied Analysis

Editor-in-Chief: Fechner, Włodzimierz / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

CiteScore 2018: 0.45

SCImago Journal Rank (SJR) 2018: 0.181
Source Normalized Impact per Paper (SNIP) 2018: 0.845

Mathematical Citation Quotient (MCQ) 2018: 0.20

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Volume 18, Issue 2


Lagrangian and Hamiltonian dynamics with imaginary time

Rami Ahmad El-Nabulsi
  • Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641112; and College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, P. R. China
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Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/jaa-2012-0010


Certain aspects of Lagrangian and Hamiltonian dynamics are investigated within the framework of an extended complex phase space approach, characterized by the transformation and by the presence of the imaginary time variable in the complex variable in a local chart. It is an application of imaginary time which is essential in connecting quantum mechanics with statistical physics. We argue that the novel complexified approach enhances the system of dynamical equations obtained in the sense that the new derived equations appear as certain combinations of former equations. Furthermore, it was shown that the physics we experience in the real time is somewhat different from what is experienced in imaginary region. Further consequences are discussed in some details.

Keywords: Complexified dynamics; imaginary time; pendulum problem

About the article

Received: 2011-06-06

Revised: 2012-04-06

Accepted: 2012-05-09

Published Online: 2012-11-27

Published in Print: 2012-12-01

Citation Information: , Volume 18, Issue 2, Pages 283–295, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/jaa-2012-0010.

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Rami Ahmad El-Nabulsi
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