Higher Time Derivative Theories From Integrable Models

TL;DR

This paper explores higher time derivative theories derived from integrable models like KdV and mKdV, analyzing their classical stability and quantization issues, revealing inherent problems such as negative norm states and unbounded Hamiltonians.

Contribution

It introduces a novel approach by generating higher time derivative theories from integrable models and studies their classical and quantum properties.

Findings

Classical solutions show stability or instability depending on parameters.

Quantization reveals negative norm states or unbounded Hamiltonian issues.

The approach links integrable models with higher derivative theories, offering new insights.

Abstract

Higher Time Derivative Theories are generated by considering space-time rotated KdV and mKdV systems. These systems are then studied to see if/how instabilities, usually associated with higher time derivative theories, manifest on the classical level by presenting both analytic and numerical solutions. For a linearised version of these space-time rotated systems we present a detailed quantisation of the theory that highlights the known dilemma on higher time derivative theories, that we have either negative norm states or the Hamiltonian being unbounded from below.