Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.Comment: 5 pages, based on the presentation on the Ninth Conference on Quantum Field Theory under the influence of External Conditions, Oklahoma, 200

Field of homogeneous Plane in Quantum Electrodynamics

We study quantum electrodynamics coupled to the matter field on singular background, which we call defect. For defect on the infinite plane we calculated the fermion propagator and mean electromagnetic field. We show that at large distances from the defect plane, the electromagnetic field is constant what is in agreement with the classical results. The quantum corrections determining the field near the plane are calculated in the leading order of perturbation theory.Comment: 16 page

Parity violating cylindrical shell in the framework of QED

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 regularization of UV divergencies of the theory we use % physically motivated Pauli-Villars regularization of the free EM action. The divergencies are extracted as a polynomial in regularization mass $M$, and they renormalize 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 $a\to\infty$ we reproduce the known results for CE for perfectly conducting cylindrical shell first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde

Casimir type effects for scalar fields interacting with material slabs

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. For the single layer system we develop a rigorous calculation method and derive explicitly the propagator of the theory, S-matrix elements and the Casimir self-energy of the slab. Detailed investigation of particular limits of self-energy is presented, and connection to know cases is discussed. The calculation method is found applicable to the two mirrors case as well. By means of it we derive the corresponding Casimir energy and analyze it. For particular values of the parameters of the model the obtained results recover the Lifshitz formula. We also propose a procedure to obtain unambiguously the finite Casimir \textit{self}-energy of a single slab without reference to any renormalizations. We hope that our approach can be applied to calculation of Casimir self-energies in other demanded cases (such as dielectric ball, etc.)Comment: 22 pages, 3 figures, published version, significant changes in Section 4.