Integral Representations For Spatial Models of Mathematical Physics: 1st Edition (Hardback) book cover

Integral Representations For Spatial Models of Mathematical Physics

1st Edition

By Vladislav V Kravchenko, Michael Shapiro

Chapman and Hall/CRC

256 pages

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Hardback: 9780582297418
pub: 1996-06-27
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This book provides a new mathematical theory for the treatment of an ample series of spatial problems of electrodynamics, particle physics, quantum mechanics and elasticity theory. This technique proves to be as powerful for solving the spatial problems of mathematical physics as complex analysis is for solving planar problems.

The main analytic tool of the book, a non-harmonic version of hypercomplex analysis recently developed by the authors, is presented in detail. There are given applications of this theory to the boundary value problems of electrodynamics and elasticity theory as well as to the problem of quark confinement. A new approach to the linearization of special classes of the self-duality equation is also considered. Detailed proofs are given throughout. The book contains an extensive bibliography on closely related topics.

This book will be of particular interest to academic and professional specialists and students in mathematics and physics who are interested in integral representations for partial differential equations. The book is self-contained and could be used as a main reference for special course seminars on the subject.

Table of Contents

Introduction and some remarks on generalisations of complex analysis

a-holomorphic function theory

Electrodynamical models

Massive spinor fields

Hypercomplex factorization, systems of non-linear partial differential equations generated by Futer-type operators.

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mathematical Physics
SCIENCE / Physics