Integral Representations For Spatial Models of Mathematical Physics

Escuela Superior de Ingenieria Mecanica y Electrica del IPN, Mexico. Escuela Superior de Fisica y Matematicas del IPN, Mexico.

0 Introduction and some remarks on generalizations of complex analysis -- 1 a-holomorphic function theory -- 1 Algebras of real and complex quaternions -- 2 Helmholtz operator with complex and quaternionic wave number -- 3 Notion of a-holomorphic function -- 4 Integral formulas for a -holomorphic functions -- 5 Boundary value properties of a-holomorphic functions -- 6 Boundary value problems for a -holomorphic functions -- 7 Vectorial reformulation of some quaternionic objects and results -- 2 Electrodynamical models -- 8 The classical Maxwell equations -- 9 Relation between electromagnetic fields and a -holomorphic functions -- 10 Integral representations of electrodynamical quantities -- 11 Boundary value problems for time-harmonic electromagnetic fields -- 3 Massive spinor fields -- 12 The classical Dirac equation and its biquaternionic reformulation -- 13 Integral representations and boundary value problems for time-harmonic spinor fields -- 14 Boundary integral criteria for the MIT bag model -- 4 Hypercomplex factorization, systems of non-linear partial differentis equations generated by Futer-type operators -- 15 Notion of hypercomplex factorization and applications to mathematical physics -- 16 Self-duality equation and other systems of non-linear partial differential equations generated by the Futer-type operators -- Appendices -- 1 Real quaternions -- 2 Representations of real quaternions -- 3 Complex quaternions -- 4 a -holomorphic functions of two real variables -- Bibliography -- Index.