Slice Dirac operator over octonions
Ming Jin, Guangbin Ren, Irene Sabadini
Abstract
Abstract The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative O (1) case to the non-commutative O (3) case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the Cauchy-Pompeiu formula), and the Taylor as well as the Laurent series expansion formulas.
Topics & Concepts
MathematicsDirac operatorClifford analysisCommutative propertyAlgebra over a fieldLaurent seriesOperator (biology)Pure mathematicsDirac algebraQuaternionDirac (video compression format)Cauchy's integral formulaKernel (algebra)Mathematical analysisDirac equationMathematical physicsCauchy problemGeometryQuantum mechanicsInitial value problemRepressorPhysicsTranscription factorChemistryNeutrinoGeneBiochemistryAlgebraic and Geometric AnalysisHolomorphic and Operator TheoryMathematical Analysis and Transform Methods