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.Comment: 13 pages, 2 figure
