Symmetries in Science X, Bruno Gruber; Michael Ramek

Автор: Bruno Gruber; Giuseppe Marmo; Naotaka Yoshinaga
Название: Symmetries in Science XI
ISBN: 9048166926 ISBN-13(EAN): 9789048166923
Издательство: Springer
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Описание: 2 Elementary systems on G-manifolds. 292 3 Two elementary systems: The(GG)-manifold and its subma- fold splitting underdiag(GG). 293 4 Examples of internal coordinates on(GG). 297 5 Kronecker products and two-particle state decompositions on(G G). 298 6 Fusion of two elementary systems on(GG). 300 7 Elementary systems on the Poincare-manifold. 301 7. 1 Mackey and covariant ?elds. 301 7. 2 From covariant to Mackey ?elds. 302 7. 3 Obstruction of Poincare-manifolds by covariant ?elds. 303 8 Relativistic position operators and coordinates. 305 8. 1 Position operators for relativistic Mackey ?elds. 305 8. 2 Position operators for ?elds with spin. 306 9 From Dirac ?elds to Bargmann-Wigner ?elds by fusion. 307 10 Elementary systems in interaction. 309 10. 1 Euclidean invariant interactions. 309 10. 2 Interacting Dirac spinor ?elds. 310 11 Scission of an elementary system. 311 12 Conclusion. 313 13 Appendix. 313 13. 1 A: Orthogonality and completeness of unitary represen- tions. 313 13. 2 B: Parameters, cosets and multiplication rules forSl(2, C). 313 13. 3 C: Observables in the relativistic 2-body system. 314 Propagation in crossed electric and magnetic ?elds 317 T. Kramer, C. Bracher 1 Introduction 317 2 Elastic scattering and quantum sources 318 2. 1 Connection to the propagator 319 2. 2 Currents generated by quantum sources 321 2. 3 Density of States 322 2. 4 Construction of the Green function 322 3 Matter waves in crossed electric and magnetic ?elds 324 3. 1 The quantum propagator 324 3.

Автор: Claus M?ller
Название: Analysis of Spherical Symmetries in Euclidean Spaces
ISBN: 1461268273 ISBN-13(EAN): 9781461268277
Издательство: Springer
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Описание: This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions.

Автор: W.I. Fushchich; A.G. Nikitin
Название: Symmetries of Maxwell`s Equations
ISBN: 9027723206 ISBN-13(EAN): 9789027723208
Издательство: Springer
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Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Автор: Claus M?ller
Название: Analysis of Spherical Symmetries in Euclidean Spaces
ISBN: 0387949496 ISBN-13(EAN): 9780387949499
Издательство: Springer
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Описание: Offers a fresh and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. This work uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. It is particularly important for the complexification of the Funk-Hecke.

Автор: Thomas Bartsch
Название: Topological Methods for Variational Problems with Symmetries
ISBN: 354057378X ISBN-13(EAN): 9783540573784
Издательство: Springer
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Описание: This monograph is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functions. These topological methods are developed in detail with new calculations and then applied to various problems. Some familiarity with basic algebraic topology is assumed.