Problems in quantum mechanics and quantum field theory with strong backgrounds and in noncommutative spacetimes

Abstract

The present project encompasses several topics in quantum mechanics and quantum field theory (QFT) with strong backgrounds and in noncommutative spacetimes. We will study creation of particles from vacuum by strong constant and non-homogeneous electric fields, including one-loop effects and backreaction on the surface of a quark star, as well as neutral particle creation with anomalous magnetic-moment in strong non-uniform magnetic fields. We will consider physical effects in classical field theory and QFT due to spacetime noncommutativity, in particular photon dispersion, birrefringence and splitting in noncommutative quantum electrodynamics. We will study noncommutative geometry in QFT, and QFT with boundaries with applications to the Casimir effect. We will also study collective excitations of neutrinos from the point of view of QFT with strong backgrounds and neutrino creation from external fields. We will investigate QFT applications to graphene physics using our experience with exact solutions of the Dirac model in external fields. We will continue the study of quantum effects of synchroton radiation. Through the development of semiclassical methods, we intend to formulate a new approach towards the construction of coherent states for systems with a continuous energy spectrum and its application to quantization. Finally, we will develop applications of the method of Man'ko's probability representation, which has attracted a lot of attention in semiclassical techniques for the problem of the motion of a charge in a electromagnetic fields. (AU)