Parity Violation and Arrow of Time in Generalized Quantum Dynamics

It is shown, that parity violation in quantum systems can be a natural result of their dynamical evolution. The corresponding (completely integrable) formalism is based on the use of quantum theory with complex time and non-Hermitian Hamiltonian. It is demonstrated, that starting with total symmetry between left and right states at the initial time, one obtains strictly polarized system at the time infinity. The increasing left-right asymmetry detects a presence of well-defined arrow of time in evolution of the system. We discuss possible application of the general formalism developed to construction of modified irreversible dynamics of massless Dirac fields (in framework of superstring theory, for example).