## Encyclopedia of mathematical physics, Volume 1The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking. |

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### Contents

Location references refer to the volume number and page number separated by a colon | 1 |

VOLUME | 4 |

Painleve Equations N Joshi | 6 |

Copyright | |

230 other sections not shown

### Common terms and phrases

abelian anomaly asymptotic bifurcation black hole boundary conditions branes bundle C*-algebra called canonical classical cohomology compact complex computed configuration consider constant coordinates corresponding D-branes defined denote density described differential equations dimensional dimensions duality dynamics energy entropy equilibrium equivalent evolution example existence fermions Figure finite function gauge theory geometry given gravity Hamiltonian Hilbert space Hopf algebra integral interaction invariant isomorphism Lagrangian lattice Lie algebra Lie group limit linear magnetic manifold Mathematical Physics matrix mechanics metric motion nonlinear normal obtained operator orbits pair parameter particles perturbation phase space piston Poisson Poisson bracket potential problem properties quantization quantum channel quantum field theory Quantum Groups relation representation satisfy scalar singularities smooth solution spacetime spin string theory structure supergravity supersymmetry surface symmetry tensor theorem thermodynamic tion topological transformation University variables vector field vector space velocity vortices wave zero