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Analysis of Dirac Systems and Computational Algebra

Author: Fabrizio Colombo; Irene Sabadini; Franciscus Sommen; Daniele C Struppa
Publisher: Boston, MA : Birkhäuser Boston : Imprint : Birkhäuser, 2004.
Series: Progress in mathematical physics, 39.
Edition/Format:   eBook : Bibliographic data : EnglishView all editions and formats
Summary:
The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science. The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Fabrizio Colombo; Irene Sabadini; Franciscus Sommen; Daniele C Struppa
ISBN: 9780817681661 0817681663 9781461264699 1461264693 0817642552 9780817642556
OCLC Number: 840276464
Description: 1 online resource (XVI, 336 pages 6 illustrations).
Contents: Preface --
Background Material --
Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations --
The Cauchy-Fueter Systems and its Variations --
Special First Order Systems in Clifford Analysis --
Some First Order Linear Operators in Physics --
Open Problems and Avenues for Further Research --
References --
Index.
Series Title: Progress in mathematical physics, 39.
Responsibility: by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa.

Abstract:

The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science. The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Grbner bases as a primary theoretical tool. Knowledge from different fields of mathematics such as commutative algebra, Grbner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented. The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.

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From the reviews:"The book presents a uniform treatment of some fundamental differential equations for physics. Maxwell and Dirac equations are particular examples that fall into this study. The Read more...

 
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