High precision calculations in quantum field theory

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The following decade is crucial for our understanding of the fundamental structure of elementary particles and forces. The Large Hadron Collider Run 2 is already taking data at unprecedented center-of-mass energy of 13 TeV, which could in a nearest future uncover principally new phenomena such as the extra space dimensions, supersymmetry, etc. On the other hand increasing accuracy of the low-energy experiments allows for a very accurate determination of the fundamental parameters of particle physics and becomes competitive in probing new physics beyond the standard model of particle interactions. In most cases the new physics may show up as a tiny deviation from the theoretical predictions based on the standard model. Thus the high precision of the predictions becomes mandatory. The main aim of the project is the calculation of the high-order perturbative corrections in a wide class of the quantum field theory problems ranging from nonrelativistic to ultrarelativistic limit, which are of primary phenomenological importance for current and future experiments. The results of the proposed research are crucial for the study of the fundamental phenomena such as the electroweak symmetry breaking and the fermion mass generation, for precise determination of the fundamental parameters of particle physics such as the heavy quark masses and the strong coupling constant, etc. The high-order analysis of the hydrogen-like bound states within quantum electrodynamics gives one of the most accurate predictions in physics to be confronted with the results of the ongoing experiments, and may provide one of the most sensitive tests of an "exotic" new physics such as the mirror universe, large extra dimensions and millicharge particles. The difficulty of the suggested problems requires developing new theoretical and computational tools, which are closely related to the fundamental concepts of the quantum field theory including the effective field theory approach, renormalization group, unstable particle production and lattice gauge theories. Deeper understanding and development of these concepts are also among the aims of the project. Many ideas of quantum field theory proved to be very useful also in modern condensed matter physics. I plan to continue the study of physical phenomena at the interface between these fields. In particular, the field theoretical methods may be crucial for determination of the accuracy of the electric current standards based on the single-electron tunneling devices, which play an important role in metrology.