Born's rule and permutation invariance

TL;DR

This paper investigates the mathematical structure of quantum probability densities, revealing a hyperbolic equation of motion with nonlocal derivatives, and explores implications for particle correlations, permutation invariance, and the quantum-classical transition.

Contribution

It introduces a hyperbolic equation for probability density with nonlocal derivatives and examines its implications for quantum correlations and the quantum to classical transition.

Findings

Probability density satisfies a hyperbolic equation of motion.

The equation involves derivatives at remote spatial regions.

Permutation invariance relates to quantum equilibrium conditions.

Abstract

It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore inter-particle correlations and the relation between the quantum equilibrium condition and the permutation invariance of the probability density. Some remarks with respect to the quantum to classical transition are also presented.