Algebraic Twistor Dynamics of Identical Singularities in a Complex Extension of the Space-Time

We present an algebraic field theory based completely on a nonlinear generalization of the Cauchy--Riemann conditions of complex analyticity to the noncommutative algebra of biquaternions. Any biquaternionic field possesses a natural twistor structure and, in the Minkowski space, gives rise to a shear-free null congruence of rays and to an associated set of gauge fields. In the article we develop this algebrodynamical scheme on the complex extension of the Minkowski space --- the full vector space of biquaternion algebra. Initial space dynamically reduces to the 6D ``observable'' space-time of the complex null cone which, in the turn, decomposes into a 4D physical space-time and 2D internal ``spin space''. In this procedure there arises an ensemble of identical point charges (``duplicons'') --- focal points of the congruence. Temporal dynamics of individual duplicons is strongly correlated via fundamental twistor field of the congruence. We briefly discuss some new notions inevitably arising in the considered algebrodynamical scheme, namely those of ``complex time'' and of ``evolutionary curve'', as well as their hypothetical connection with the quantum uncertainty phenomena.