Higher-order Lorentz-invariance violation, quantum gravity and fine-tuning

The issue of Lorentz fine-tuning in effective theories containing higher-order operators is studied. To this end, we focus on the Myers-Pospelov extension of QED with dimension-five operators in the photon sector and standard fermions. We compute the fermion self-energy at one-loop order considering its even and odd $CPT$ contributions. In the even sector we find small radiative corrections to the usual parameters of QED which also turn to be finite. In the odd sector the axial operator is shown to contain unsuppressed effects of Lorentz violation leading to a possible fine-tuning. We use dimensional regularization to deal with the divergencies and a generic preferred four-vector. Taking the first steps in the renormalization procedure for Lorentz violating theories we arrive to acceptable small corrections allowing to set the bound $\xi<6 \times10^{-3}$.Comment: 11 pages, new version with the correct pole extractio

Polymer quantization, stability and higher-order time derivative terms

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

Electromagnetic interactions with an electrically uniaxial composite layering

International audienceA 3-D mathematical model is developed for fields due to currents in the presence of a planarly stratified composite medium. General expressions for the dyadic Green's functions in the case of a non-magnetic, electrically uniaxial type of anisotropy are derived herein as a necessary first step. The associated electric-electric dyadic Green's function is constructed from transverse electric and transverse magnetic scalar modes using interface and radiation (at infinity) conditions. The regular part of the electric-electric dyadic Green's function is computed by a Fast Fourier Transform technique and is used to calculate the electromagnetic response of a planarly composite material having a delamination of various thickness at a given interface