Higher order topological actions

TL;DR

This paper introduces an infinite sequence of higher order topological actions in classical mechanics, explores their potential role in quantum mechanics, and suggests they could be experimentally observed.

Contribution

It constructs a new hierarchy of topological actions and discusses their significance in quantum mechanics, extending the understanding of topological effects.

Findings

Higher order topological actions form an infinite sequence.

These actions can influence quantum phenomena.

Potential for experimental detection of higher order topological effects.

Abstract

In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological actions and argue that they play a role in quantum mechanics, and hence can be accessed experimentally.