Russian Journal of Mathematical Physics

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

Abdelouahab Kenoufi, Michel Gondran, Alexandre Gondran

Published Jan 1, 2020• 2 citations

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.

DOI: 10.1134/s1061920820010069

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