Action for classical, quantum, closed and open systems

TL;DR

This paper explores a unified action-based framework for classical, quantum, closed, and open systems, emphasizing the role of degree-of-freedom redoubling in variational and path integral formalisms.

Contribution

It introduces a generalized action formalism that naturally incorporates the redoubling of degrees of freedom for diverse dynamical systems.

Findings

Unified description of classical and quantum dynamics via action principles

Justification of degree-of-freedom redoubling in variational and path integral approaches

Applicability to both closed and open systems

Abstract

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics, respectively. These schemes are based on an unusual feature, a formal redoubling of the degrees of freedom. Several arguments to motivate the redoubling are put forward in classical and quantum mechanics to demonstrate that such a formalism is natural.