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Analysis of Dirac Systems and Computational Algebra (Progress in Mathematical Physics)
Analysis of Dirac Systems and Computational Algebra - Progress in Mathematical Physics Author:Fabrizio Colombo, Irene Sabadini, Frank Sommen, Daniele C. Struppa Since their inception, Clifford algebras have been used as a mathematical tool for the description of physical phenomena. However, Clifford algebras have 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 sci... more »ence as well. This book details: Systems of first-order linear differential equations that arise naturally in the setting of Clifford algebras; some well-known systems that play a role in electromagnetism and quantum mechanics, and others that figure prominently in harmonic analysis. The reader is also introduced to new classes of special first order differential equations that have never been studied before, with applications ranging from multiparticle theory to finite geometry.These powerful new tools are applied to the study of Dirac and Dirac-like systems, Maxwell and Proca systems, and higher spin systems such as the Rarita-Schwinger system. Given the richness of new ideas and research problems, this work should serve advanced undergraduates and graduate students in mathematics, physics and computer science, as well as researchers in Clifford analysis, differential equations, Grobner bases, computer algebra, quantum field theory and microlocal analysis. Only a basic course in complex analysis is required; the fundamentals of Clifford analysis are provided.« less