MG11 
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THE CASIMIR EFFECT IN RELATIVISTIC QUANTUM FIELD THEORIES

We discuss the recent developments in the Casimir effect which arises in restricted quantization volumes and in spaces with nontrivial topology. During the time after MG10 this field of physics was quickly developing. The most important advances were achieved in the measurements of the Casimir force, in theoretical understanding of the Casimir interaction between real materials, in obtaining new exact solutions for curved boundaries, and in constraining new physics beyond the Standard Model using the achieved agreement of experiment and theory. The main results obtained in these scientific directions will be discussed in the talk. The special attention will be paid to the outstanding fundamental problems arising at the frontiers between the Matsubara quantum field theory, statistical physics and thermodynamics.