Polymer quantization, stability and higher-order time derivative terms

TL;DR

This paper explores how polymer quantization, a nonstandard quantum representation, can potentially stabilize higher-order time derivative theories like the Pais-Uhlenbeck model by addressing issues of negative energy and instability.

Contribution

It demonstrates that polymer quantization introduces new stable regions in the Hamiltonian of higher-order theories, potentially resolving longstanding stability issues.

Findings

Polymer quantization can bound the Hamiltonian from below.

New stable regions are identified in the Pais-Uhlenbeck model.

The approach may mitigate negative energy problems in higher-order theories.

Abstract

The stability of higher-order time derivative theories using the polymer extension of quantum mechanics is studied. First, we focus on the well-known Pais-Uhlenbeck model and by casting the theory into the sum of two decoupled The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation, called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories; rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrodinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.