Unitarity, ghosts and nonminimal terms in Lorentz violating QED

The unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.Comment: Presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 201

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

Predictive control of a solar air conditioning plant with simultaneous identification

This paper presents the application of a predictive controller with simultaneous identification to a solar air conditioning plant. The time varying nature of the process makes necessary an adjustment of the controller parameters to the varying operational conditions. The main novelty with respect to classic adaptive MPC scheme is to penalize the identification error in the cost function used for control. The behaviour of the controller is illustrated by simulations and experimental results. The integration of identification and control avoids the tedious identification procedure that is necessary before the start-up of any predictive controller. This new adaptive MPC scheme shows its effectiveness in controlling the outlet temperature in the solar thermal plant.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-0