Low energy Lorentz violation in polymer quantization revisited

In previous work, it had been shown that polymer quantized scalar field theory predicts that even an inertial observer can experience spontaneous excitations. This prediction was shown to hold at low energies. However, in these papers it was assumed that the polymer scale is constant. But it is possible to relax this condition and obtain a larger class of theories where the polymer scale is a function of momentum. Does the prediction of low energy Lorentz violation hold for all of these theories? In this paper we prove that it does. We also obtain the modified rates of radiation for some of these theories.