Author | Colombo, Fabrizio. author |
---|---|
Title | Analysis of Dirac Systems and Computational Algebra [electronic resource] / by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8166-1 |
Descript | XV, 332 p. online resource |
1 Background Material -- 1.1 Algebraic tools -- 1.2 Analytical tools -- 1.3 Elements of hyperfunction theory -- 1.4 Appendix: category theory -- 2 Computational Algebraic Analysis -- 2.1 A primer of algebraic analysis -- 2.2 The Ehrenpreis-Palamodov Fundamental Principle -- 2.3 The Fundamental Principle for hyperfunctions -- 2.4 Using computational algebra software -- 3 The Cauchy-Fueter System and its Variations -- 3.1 Regular functions of one quaternionic variable -- 3.2 Quaternionic hyperfunctions in one variable -- 3.3 Several quaternionic variables: analytic approach -- 3.4 Several quaternionic variables: an algebraic approach -- 3.5 The Moisil-Theodorescu system -- 4 Special First Order Systems in Clifford Analysis -- 4.1 Introduction to Clifford algebras -- 4.2 Introduction to Clifford analysis -- 4.3 The Dirac complex for two, three and four operators -- 4.4 Special systems in Clifford analysis -- 5 Some First Order Linear Operators in Physics -- 5.1 Physics and algebra of Maxwell and Proca fields -- 5.2 Variations on Maxwell system in the space of biquaternions -- 5.3 Properties of DZ-regular functions -- 5.4 The Dirac equation and the linearization problem -- 5.5 Octonionic Dirac equation -- 6 Open Problems and Avenues for Further Research -- 6.1 The Cauchy-Fueter system -- 6.2 The Dirac system -- 6.3 Miscellanea