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

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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Submitted on : Monday, July 20, 2020 - 10:13:41 AM
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Abdelouahab Kenoufi, Michel Gondran, Alexandre Gondran. Semi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle Duality. Russian Journal of Mathematical Physics, MAIK Nauka/Interperiodica, 2020, 27 (1), pp.61-75. ⟨10.1134/S1061920820010069⟩. ⟨hal-02892760⟩

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