Time evolution of density matrices as a theory of random surfaces

TL;DR

This paper reveals that Marinov's path integral, used for quantum density matrix evolution, inherently describes a theory of ruled random surfaces in phase space, offering new geometric insights into quantum dynamics.

Contribution

It uncovers a hidden geometric property of Marinov's path integral, linking quantum density matrix evolution to a theory of random surfaces in phase space.

Findings

Marinov's path integral describes ruled random surfaces in phase space.

The work provides a new geometric interpretation of quantum evolution.

It bridges operator formalism and geometric surface theories in quantum mechanics.

Abstract

In the operatorial formulation of quantum statistics, the time evolution of density matrices is governed by von Neumann's equation. Within the phase space formulation of quantum mechanics it translates into Moyal's equation, and a formal solution of the latter is provided by Marinov's path integral. In this paper we uncover a hidden property of the Marinov path integral, demonstrating that it describes a theory of ruled random surfaces in phase space.