Lambrecht, Astrid; Marachevsky, Valery N. Theory of the Casimir effect in one-dimensional periodic dielectric systems. (English) Zbl 1170.81409 Int. J. Mod. Phys. A 24, No. 8-9, 1789-1795 (2009). Summary: We derive an exact theory of the Casimir interaction between two arbitrary dielectric gratings with coinciding periods d. We then express the Casimir energy for two dielectric gratings or periodic dielectrics with coinciding periods in terms of Rayleigh coefficients. Cited in 2 Documents MSC: 81T05 Axiomatic quantum field theory; operator algebras 81T99 Quantum field theory; related classical field theories 81V10 Electromagnetic interaction; quantum electrodynamics Keywords:Casimir force; Rayleigh coefficients PDFBibTeX XMLCite \textit{A. Lambrecht} and \textit{V. N. Marachevsky}, Int. J. Mod. Phys. A 24, No. 8--9, 1789--1795 (2009; Zbl 1170.81409) Full Text: DOI References: [1] Casimir H. B. G., Proc. K. Ned. Akad. Wet. 51 pp 793– [2] Barton G., Rep. Prog. Phys. 42 pp 65– [3] DOI: 10.1103/PhysRevLett.94.110404 [4] DOI: 10.1103/PhysRevA.69.023808 [5] DOI: 10.1088/0305-4470/39/21/S08 · Zbl 1094.82017 [6] Henkel C., EPL 9 pp 929– [7] DOI: 10.1088/1367-2630/9/8/254 [8] DOI: 10.1088/1751-8113/41/16/164015 · Zbl 1137.81397 [9] DOI: 10.1103/PhysRevLett.100.183602 [10] DOI: 10.1016/0370-1573(86)90020-7 [11] Lifshitz E. M., Soviet Phys. JETP 2 pp 73– [12] DOI: 10.1007/s100530050041 [13] DOI: 10.1103/PhysRevA.62.014102 [14] Büscher R., Nucl. Phys. B 696 pp 468– [15] DOI: 10.1103/PhysRevA.77.013811 [16] DOI: 10.1103/PhysRevLett.99.170403 [17] Emig T., J. Stat. Mech. pp P04007– [18] DOI: 10.1103/PhysRevA.67.043811 [19] DOI: 10.1103/PhysRevA.78.012115 [20] DOI: 10.1088/1367-2630/8/10/243 [21] DOI: 10.1103/PhysRevLett.87.211801 [22] DOI: 10.1103/PhysRevLett.101.030401 [23] DOI: 10.1016/0375-9601(73)90307-1 [24] DOI: 10.1070/PU1975v018n05ABEH001958 [25] DOI: 10.1016/S0370-1573(01)00015-1 · Zbl 0972.81212 [26] DOI: 10.1098/rspa.1907.0051 · JFM 38.0842.03 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.