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Semi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle Duality

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Abstract

One shows that the Feynman’s Path Integral designed for quantum mechanics has an analogous in classical mechanics, the so-called (min, +) Path Integral. This former is build on (min, +)-algebra and (min, +)-analysis which permit to handle in a linear way non-linear problems occurring in mathematical physics. The Hamilton-Jacobi equations and their solutions within this mathematical framework, are introduced and yield to a new interpretation expressed in a duality between action field and particle.

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Acknowledgements

We thank Professors Lyazid Chetouani, Janos Polonyi, and René Voltz for interesting and useful discussions about path integrals and least-action principles.

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Authors and Affiliations

  1. Scientific Consulting for Research & Engineering (SCORE), Strasbourg, France

    A. Kenoufi

  2. European Interdisciplinary Academy of Sciences (EIAS), Paris, France

    A. Kenoufi & M. Gondran

  3. Ecole Nationale de l’Aviation Civile (ENAC), Toulouse, France

    A. Gondran

Authors
  1. A. Kenoufi
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  2. M. Gondran
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  3. A. Gondran
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Correspondence to A. Kenoufi, M. Gondran or A. Gondran.

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Kenoufi, A., Gondran, M. & Gondran, A. Semi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle Duality. Russ. J. Math. Phys. 27, 61–75 (2020). https://doi.org/10.1134/S1061920820010069

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  • DOI: https://doi.org/10.1134/S1061920820010069

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