currently under peer review by EIT

 

ABSTRACT: In this review endeavor, we present the recently suggested signed particle formulation, reviving the Wigner’s formulation of quantum mechanics by looking at it from a new point of view. The new theory describes quantum systems by means of ensembles of Newtonian field-less particles, which have a position, a momentum, and carry a sign. The signed particle formulation is equivalent to the conventional formulations of quantum mechanics and the predictions derived from this theory are exactly the same as those from other more standard approaches (without involving the concept of wave-functions). Important advantages of the signed particle formalism include the ability to simulate complex quantum systems by means of relatively small computational resources. We present the set of postulates, which completely define the formulation and two of the many possible applications of this theory. The applications relate to systems of identical Fermions and the Pauli exclusion principle, as well as the hydrogen atom beyond the Born-Oppenheimer approximation. We conclude with a future outlook.