Spin-like current from phase space distributions

TL;DR

This paper explores a phase space approach to quantum currents, revealing how different distribution functions influence local current expressions and demonstrating conditions under which they align with traditional spin-1/2 currents.

Contribution

It introduces a generalized phase space framework for quantum currents, identifying restrictions for distribution functions to recover standard spin-1/2 current behavior.

Findings

The current depends on the choice of distribution function.

Continuity equation constrains admissible distributions.

Certain non-bilinear distributions match the spin-1/2 current in specific limits.

Abstract

The spin 0 generalized phase space approach provides a general expression for local current which depends on the choice of distribution function and generally deviates from the Schrodinger current. It is shown that the continuity equation restricts the admissible bilinear distributions such that the current has a unique dependence on the wavefunction and coincides with the non-relativistic limit of the relativistic spin 1/2 current for a spin eigenstate, up to a constant vector. Examples of non-bilinear distributions that have the latter property are given.