Abstract
The aim of the project is two-fold. We shall develop the methods of quantum theory and also apply these methods to some interesting problems of modern physics. A considerable part of the project is dedicated to non perturbative quantum electrodynamics. The cases of strong external field and of non-linear quantum theory will be treated in detail. The prominent place occupied by this topic is related to its' role in the front-line physics research including the physics of dense stars and hadronic matter, as well as the physics of graphene. The physics of new materials - graphene, topological insulators and Weyl semimetals - is considered in separate Chapter in this project. The spectrum of excitations in these materials is described by the Dirac equation, which makes Quantum Field Theory the most adequate theoretical tool and connects this research to other parts of the project. Most of our calculations here (the Casimir effect, optical properties, conductivity) will admit immediate experimental verification. The holographic principle has less connections with the current experiments, but no less interesting. Though this principle was suggested in String Theory, our consideration has a broader context. We shall analyze many, mostly low-dimensional, holographic models and check their consistency. The practical tool here is non-perturbative (in the AdS radius) calculations in QFT, similar to the rest of the project. The part related to noncommutative geometry is on the cross-road with pure mathematics: we shall use the advances in mathematics (as the deformation quantization and formality) to address physics problems and utilize the QFT techniques for the purposes of mathematics. (AU)
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