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

Abdelouahab Kenoufi (1) , Michel Gondran (2) , Alexandre Gondran (3)

1 SCORE
2 EIAS - European Interdisciplinary Academy of Sciences
3 ENAC - Ecole Nationale de l'Aviation Civile

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

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, 2020, 27 (1), pp.61-75. ⟨10.1134/S1061920820010069⟩. ⟨hal-02892760⟩