[en] We show that the presence of parity-odd terms in the conductivity (i.e. in the polarization tensor of Dirac quasiparticles in graphene) leads to the rotation of polarization of the electromagnetic waves passing through suspended samples of graphene. Parity-odd Chern-Simons-type contributions appear in external magnetic fields, giving rise to a quantum Faraday effect (though other sources of parity-odd effects may also be discussed). The estimated order of the effect is well above the sensitivity limits of modern optical instruments. (fast track communication)

[en] We study the field theoretical model of a scalar field in the presence of spacial inhomogeneities in the form of one and two finite-width mirrors (material slabs). The interaction of the scalar field with the defect is described with a position-dependent mass term. For a single-layer system we develop a rigorous calculation method and derive explicitly the propagator of the theory, the S-matrix elements and the Casimir self-energy of the slab. Detailed investigation of particular limits of self-energy is presented, and the connection to known cases is discussed. The calculation method is also found applicable to the two-mirror case. With its help we derive the corresponding Casimir energy and analyze it. For particular values of parameters of the model an obtained result recovers the Lifshitz formula. We also propose a procedure to unambiguously obtain the finite Casimir self-energy of a single slab without reference to any renormalization conditions. We hope that our approach can be applied to the calculation of Casimir self-energies in other demanded cases (such as a dielectric ball, etc).

[en] It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE), which, in addition, may be represented as one in momentum space composed of the two point Green’s functions. We propose the generalization of this expression to the QHE in the presence of non-uniform magnetic field. The proposed expression is the topological invariant in phase space composed of the Weyl symbols of the two-point Green’s function. It is applicable to a wide range of non-uniform tight-binding models, including the interacting ones. (paper)

[en] We study quantum electrodynamics coupled to the matter field on a singular background, which we call defect. For defect on an infinite plane we calculated the mean electromagnetic field. Quantum corrections determining the field near the plane are calculated in the leading order of perturbation theory. We analyse the normalization conditions for the parameters of the defect and calculate the photoelectric function of the charged particle from the defect

[en] We present calculations of Casimir energy (CE) in a system of quantized electromagnetic (EM) field interacting with an infinite circular cylindrical shell (which we call 'the defect'). Interaction is described in the only QFT-consistent way by Chern-Simon action concentrated on the defect, with a single coupling constant a. For the regularization of UV divergencies of the theory, we use the Pauli-Villars regularization of the free-EM action. The divergencies are extracted as a polynomial in the regularization mass M, and they renormalize the classical part of the surface action. We reveal the dependence of CE on the coupling constant a. Corresponding Casimir force is attractive for all values of a. For a → ∞, we reproduce the known results for CE for perfectly conducting cylindrical shell first obtained by DeRaad and Milton. As a future task for solving existing arguments on observational status of (rigid) self-pressure of a single object, we propose for investigation a system which we call 'Casimir drum'