Myers-Pospelov Model as an Ensemble of Pais-Uhlenbeck Oscillators: Unitarity and Lorentz Invariance Violation

We study a generalization of the Pais-Uhlenbeck oscillator for fermionic variables. Next, we consider an ensemble of these oscillators and we identify a particular case of the Myers-Pospelov model which is relevant for effective theories of quantum gravity. Finally, by taking advantage of this connection, we analyze, for this model, unitarity at one loop order in the low energy regime where no ghost states can be created on-shell. This energy regime is the relevant one when we consider the Myers-Pospelov model as a true effective theory coming from a new space-time structure. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.