We consider various aspects of construction of quantum fieldtheory (QFT) in the presence of matter with sharp boundaries and/or spatialheterogeneities. Such systems are essential in description ofCasimir interaction of (im)perfect materials, in cosmological models withnon-trivial topology of the space-time and in brane-world scenarios.It also has applications in condensed matter physics and critical phenomena.To describe the interaction of quantum fields with spatialheterogeneities we introduce singular potentials into the action of the model. Suchpotentials generalize the notions of boundary conditions. For thecase of the simplest potential of delta-function profile(representing two-dimensional surfaces) we will consider localproperties of the system such as pressure on local deformations,the energy density, etc. For the case of path-wise constantpotentials (describing volume imperfections) we will approach the problemof calculation of the Casimir energy both for scalar fields, and for QuantumElectrodynamics (QED) in presence of matter with the most general magnito-electricproperties.
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