General Rule for Boundary conditions from the Action Principle

TL;DR

This paper proposes a novel method to derive initial and boundary conditions directly from the action principle, eliminating the need for assumed constraints in physical models.

Contribution

It introduces a new rule for obtaining boundary conditions from the action principle, demonstrated through examples, including both historical and new models.

Findings

Boundary conditions can be derived from the action principle without assumptions.

The method applies to physical models represented by actions.

Examples show the practicality of the approach.

Abstract

We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical view point, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples which can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.