  We present a scheme of biquaternionic algebrodymamics based on a nonlinear
generalization of the Cauchy-Riemann holomorphy conditions considered therein
as fundamental field equations. The automorphism group SO(3,C) of the
biquaternion algebra acts as a proper Lorentz group on a real space whose
coordinates are bilinear in the complex coordinates of biquaternionic vector
space. A new invariant of Lorentz transformations then arises - the geometric
phase. This invariant can be responsible for the quantum properties of
particles associated in this approach with field singularities. Some new
notions are introduced, related to ``hidden'' complex dynamics: ``observable''
space-time, the ensemble of identical correlated particles-singularities
(``duplicons'') and others.
