The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford Classic Texts in the Physical Sciences)

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This book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanical study of a particle or quasi-particle in a molecule or crystalline solid because the eigenvalues and eigenfunctions of a system belong to the irreducible representations of the group of symmetry operations of that system. The theory is applied to give complete tables of these representations for all the 32 point groups and 230 space groups, including the double-valued representations. For the space groups, the group of the symmetry operations of the k vector and its irreducible representations are given for all the special points of symmetry, lines of symmetry and planes of symmetry in the Brillouin zone. Applications occur in the electronic band structure, phonon dispersion relations and selection rules for particle-quasiparticle interactions in solids. The theory is extended to the corepresentations of the Shubnikov (black and white) point groups and space groups.

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Arthur P. Cracknell graduated in Physics from the University of Cambridge in 1961, took his DPhil from the University of Oxford in 1964 and worked in the Physics Departments of the University of Singapore and the University of Essex before moving to Dundee as senior lecturer in 1970. He was promoted to Reader in 1974 and to Professor of Theoretical Physics in 1978 and later was transferred to the Carnegie Chair of Physics in the Department of Applied Physics and Electronic & Mechanical Engineering at Dundee University. He retired in 2002. He has won the Society Medal, The Remote Sensing Society, 1989; the Schiwefdsky Medal of the German Photogrammetric Society/ISPRS, 1996, and the President's award, Remote Sensing Society, 1996.Christopher J. Bradley won the Mayhew Prize for Distinction in Applied Mathematics, Cambridge, in 1959, before becoming Fellow in Applied Mathematics, Jesus College and CUF Lecturer in Mathematics, Oxford 1963-80. He later joined the teaching profession, and was Head of Mathematics, then Director of Studies, at Clifton College, Bristol, 1981-2003. He is a Fellow of the Institute of Mathematics and its Applications.