  The intention of this study is the search for signatures of the chiral phase
transition in heavy-ion collisions. To investigate the impact of fluctuations,
e.g., of the baryon number, at the transition or at a critical point, the
linear sigma model is treated in a dynamical (3+1)-dimensional numerical
simulation. Chiral fields are approximated as classical mean fields, and quarks
are described as quasi particles in a Vlasov equation. Additional dynamics is
implemented by quark-quark and quark-sigma-field interactions. For a consistent
description of field-particle interactions, a new Monte-Carlo-Langevin-like
formalism has been developed and is discussed.
