Vladimir V. Kisil
Connection between Different Function Theories in Clifford Analysis
(29K, LaTeX2e)

ABSTRACT.  We describe an explicit connection between solutions to equations
$Df=0$ (the Generalized Cauchy-Riemann equation) and $(D+M)f=0$, where
operators $D$ and
$M$ commute. The described connection allows to construct a ``function
theory'' (the Cauchy theorem, the Cauchy integral, the Taylor and
Laurent series etc.) for solutions of the second equation from the
known function theory for solution of the first 
(generalized Cauchy-Riemann) equation.
As well known, many physical equations related to the orthogonal group
of rotations or the Lorentz group (the Dirac equation, the Maxwell
equation etc.) can be naturally formulated in terms of the Clifford
algebra. For them our approach gives an explicit connection between
solutions  with zero and non-zero mass (or external fields) and
provides with a family of formulas for calculations.
\keywords{Dirac equation with mass, Clifford analysis.}
\AMSMSC{30G35}{34L40, 81Q05}