Quantum mechanics of higher derivative systems and total derivative terms

TL;DR

This paper develops a general quantum mechanical framework for higher derivative systems, demonstrating that Lagrangians differing by a total derivative are equivalent at the quantum level.

Contribution

It introduces a comprehensive theory showing the quantum equivalence of higher derivative Lagrangians differing by total derivatives.

Findings

Higher derivative systems are quantized within a unified framework

Lagrangians differing by total derivatives are quantum mechanically equivalent

The theory applies to singular, non-autonomous systems

Abstract

A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their difference is a total derivative.