Scope of the action principle

TL;DR

The paper explores how auxiliary variables enable deriving equations of motion from an action principle, illustrating methods with examples and applying them to Bohmian mechanics, including gauge theory formulations.

Contribution

It systematically examines methods to incorporate auxiliary variables into action principles, with applications to Bohmian mechanics and gauge theories.

Findings

Auxiliary variables facilitate deriving equations from an action principle.

Gauge theory formulation introduces gauge degrees of freedom.

Application to Bohmian mechanics demonstrates the approach's versatility.

Abstract

Laws of motion given in terms of differential equations can not always be derived from an action principle, at least not without introducing auxiliary variables. By allowing auxiliary variables, e.g. in the form of Lagrange multipliers, an action is immediately obtained. Here, we consider some ways how this can be done, drawing examples from the literature, and apply this to Bohmian mechanics. We also discuss the possible metaphysical status of these auxiliary variables. A particularly interesting approach brings the theory in the form of a gauge theory, with the auxiliary variables as gauge degrees of freedom.