Author | Kupershmidt, B. A. author |
---|---|

Title | Elements of Superintegrable Systems [electronic resource] : Basic Techniques and Results / by B. A. Kupershmidt |

Imprint | Dordrecht : Springer Netherlands, 1987 |

Connect to | http://dx.doi.org/10.1007/978-94-009-3799-4 |

Descript | XVI, 187 p. online resource |

SUMMARY

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 final question. G. K. Chesterton. The Scandal of Father 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik'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

CONTENT

I. Classical Superintegrable Systems -- ยง1. Introduction -- ยง2. Variational Calculus with Anticommuting Variables -- ยง3. SuperHamiltonian Formalism and Infinite-Dimensional Stable Lie Superalgebras -- ยง4. Residue Calculus in Modules of Differential Forms over Superalgebras of Pseudo-Differential Operators -- ยง5. Classical Superintegrable Systems -- ยง6. Variational Derivatives of Conservation Laws and the SuperHamiltonian Structure of Classical Superintegrable Systems -- II. Lie Algebras, Korteweg-De Vries Equations, and Bi-Superhamiltonian Systems -- ยง7. Three Constructions -- ยง8. Lie-Algebraic Identities -- ยง9. Bi-SuperHamiltonian Systems -- Appendix. Metrizable Lie Algebras -- Sources

Mathematics
Mathematical analysis
Analysis (Mathematics)
Physics
Mathematics
Analysis
Theoretical Mathematical and Computational Physics