Irrotational Momentum Fluctuations Conditioning the Quantum Nature of Physical Processes

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt, so that the quantum mechanical framework resembles to a large extent that of the classical statistical mechanics and hydrodynamics. The main assumption used here is the existence of a random irrotational component in the classical momentum. Various basic elements of the quantum formalism (calculation of expectation values, the Heisenberg uncertainty principle, the correspondence principle) are recovered by applying traditional techniques, borrowed from classical statistical mechanics.