Variational calculus with fractional action

Abstract

The principle of the least fractional action δ{D - 1 - i / λ (Ψ(λ))} = 0 is constructed on Ω-space. This comes from the fact that the action is introduced as a form of entropy. Non-local behavior and breakdown of the causality in this space are reviewed. The deduction of Schrodinger's equation from this formalism is presented. This work would enable us to think that quantum mechanics would be a statistical consequence of a more profound discrete deterministic theory in the same sense that thermodynamics is a consequence of the kinetic gas theory.