Polymer quantization, stability and higher-order time derivative terms

Understand

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.