This volume is the seventh in a series of proceedings on theoretical physics related to various aspects of the structure of condensed matter and to appropriate mathematical methods for adequate description. Three main topics are considered: conformal symmetry, central charge, condensation of flux; rigged string configurations, Yang-Baxter equations and their applications in solid state physics; and energy band structure in solids.

This volume continues the series of proceedings of summer schools on theoretical physics which aim at an adequate description of the structure of condensed matter in terms of sophisticated, advanced mathematical tools. This time, the main emphasis is put on the question of whether (and when) the energy bands in solids are continuous. Profs. L Michel, J Zak and others consider the origin, existence and continuity of band structure. Also, some previously discussed problems (magnetic symmetry, flux quantization, statistics, quasicrystals, the Bethe ansatz) are pursued further, and appropriate mathematical tools, rooted in “actions of groups on sets”, are developed.

These proceedings review the recent developments in current research connected with an adequate description of condensed matter in statistics of quasiparticles, topological invariants and self-similar structures.

This volume provides an adequate mathematical description of solid state properties. It concentrates on group action methods, generalized statistics and molecular symmetries (unitary and symmetric groups).

This volume is the seventh in a series of proceedings on theoretical physics related to various aspects of the structure of condensed matter and to appropriate mathematical methods for adequate description. Three main topics are considered: conformal symmetry, central charge, condensation of flux; rigged string configurations, YangOCoBaxter equations and their applications in solid state physics; and energy band structure in solids."

This volume reviews some selected problems in solid state physics with an emphasis on adequate mathematical tools. The three main subjects are magnetic structures and neutron scattering; Berry phases and energy bands in solids (symmetry, analicity, Hofstadter butterfly, van Hove singularities); and quasicrystals, finite systems, and group action on sets (unitary group approach, Schur functions). Software presentations are included as a separate part.

This volume continues the series of proceedings of summer schools on theoretical physics related to various aspects of the structure of condensed matter, and to appropriate mathematical methods for an adequate description. Three main topics are covered: (i) symmetric and unitary groups versus electron correlations in multicentre systems; (ii) conformal symmetries, the Bethe ansatz and quantum groups; (iii) paradoxes of statistics, space-time, and time quantum mechanics. Problems considered in previous schools are merged with some new developments, like statistics with continuous Young diagrams, the existence and structure of energy bands in solids with fullerenes, membranes and some coverings of graphite sheets, or vortex condensates with quantum counterparts of Maxwell lows.

This volume continues the series of proceedings of summer schools on theoretical physics related to various aspects of the structure of condensed matter, and to appropriate mathematical methods for an adequate description. Three main topics are covered: (i) symmetric and unitary groups versus electron correlations in multicentre systems; (ii) conformal symmetries, the Bethe ansatz and quantum groups; (iii) paradoxes of statistics, space-time, and time quantum mechanics. Problems considered in previous schools are merged with some new developments, like statistics with continuous Young diagrams, the existence and structure of energy bands in solids with fullerenes, membranes and some coverings of graphite sheets, or vortex condensates with quantum counterparts of Maxwell lows.

The contents survey the achievements and research problems connected with an adequate description of condensed matter structure, its phases and other properties in terms of appropriate mathematical tools. The focus is on the following topics: Action of groups on sets and broken symmetries; Racah-Wigner approach to vibrations, electronic states, correlations and superconductivity in multicenter systems; crystallography and its extension.

Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.