Abstract. Corrections to the average kinetic energy of atomic electrons caused by the change in electron mass in the photonic crystal medium are investigated. Corresponding shift of energy levels of atoms placed in a photonic crystal is shown to be of order of the ordinary Lamb shift.The investigation of photonic crystals (PC) is an actual problem today. The main feature of such media is the periodic modulation of dielectric constant along one, two or three directions of space. It yields to the range of forbidden frequencies in a material called photonic band-gaps (PBG). Unusual optical properties of the PC medium stimulate a wide range of its practical applications [1]. Another interesting field of study is quantum electrodynamics (QED) in PC medium. It has been shown that modification of photon density of states (DOS) in PC's lead to the strong emitter-photon coupling [2][3][4], coherent control of spontaneous emission [5][6][7], appearance of photon-atom bound states [2,8,9] etc. Special attention was given to the modification of the Lamb shift [2,8,[10][11][12][13][14] in atoms placed in the photonic crystal medium. By definition the Lamb shift in atoms is caused by the QED corrections to the Coulumb interaction between electrons and the atomic nucleus (see figure 1a) that gives the leading order contribution to the energy of atomic states. This interaction is modified by the processes in which the virtual photons come into play (see figure 1b). The contribution to atomic energy levels from these processes is just the Lamb shift. In principle one should account for the processes of the self interaction of the atomic electrons shown in figure 1c. In the case of atoms in free space these processes contribute only to the electron mass and are subtracted by the counter-terms of the renormalization. However, as it has been shown in Ref.[15], a modification of the of the interaction of the electron with its own radiation field in a PC gives rise to the fact that contributions from the processes in a PC shown in figure 1c differ profoundly from those in free space, and, as a result, these self-energy processes can play an important role. First of all, they change the mass of an electron in the PC medium [15]. In addition they contribute to the kinetic energy of atomic electrons in the PC. The aim of this paper is to investigate this correction to the energy levels of atoms in the PC medium.The change of the value of the kinetic energy of an electron δE is the difference between its values in the PC medium and in vacuum:

The problem is considered of describing the dynamics of quantum systems generated by a nonlocal in time interaction. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to extend quantum dynamics to describe the time evolution in the case of such interactions. In this way, using only the current concepts of quantum theory, a generalized equation of motion for state vectors is derived. In the case, where the fundamental interaction generating the dynamics in a system is local in time, this equation is equivalent to the Schrödinger equation. Explicit examples are given for an exactly solvable model. The proposed formalism is shown to provide a new insight into the problem of the description of nonlocal interactions in quantum field theory. It is shown that such a property of the equation of motion as nonlocality in time may be important for describing hadron-hadron interactions at low and intermediate energies.

Photonic crystals are periodic systems that consist of dielectrics with different refractive indices. They are designed to act on photons in contrast to semiconductor crystals whose periodicity affects the motion of electrons. Here we consider the interaction of an atomic electron with its own radiation field in the case when the atom is placed in air voids of a photonic crystal and is not in mechanical contact with the vibrational degrees of freedom of the dielectric host. A strong modification of this interaction from that in free space is shown to change the rest mass of the electron, and this has a significant effect on the shift of the atomic energy levels. This shift is investigated by using the example of atomic hydrogen in a high-index-contrast photonic crystal. The found effect may be of interest both from fundamental and practical points of view.

We investigate low energy nucleon dynamics in the effective field theory (EFT) of nuclear forces. In leading order of the two-nucleon EFT we show that nucleon dynamics is governed by the generalized dynamical equation with a nonlocal-in-time interaction operator. This equation is shown to open new possibilities for applying the EFT approach to the description of low energy nucleon dynamics.