https://hal-enac.archives-ouvertes.fr/hal-02892760Kenoufi, AbdelouahabAbdelouahabKenoufiSCORE - Scientific Consulting for Research and EngineeringGondran, MichelMichelGondranEIAS - European Interdisciplinary Academy of SciencesGondran, AlexandreAlexandreGondranENAC - Ecole Nationale de l'Aviation CivileSemi-Classical Limit and Least Action Principle Revisited with (min,+) Path Integral and Action-Particle DualityHAL CCSD2020[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Porte, Laurence2020-07-20 10:13:412021-11-03 05:38:152020-07-21 09:19:55enJournal articleshttps://hal-enac.archives-ouvertes.fr/hal-02892760/document10.1134/S1061920820010069application/pdf1One shows that the Feynmanâ€™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.