  We derive a multiconfigurational time-dependent Hartree theory for systems
with particle conversion. In such systems particles of one kind can convert to
another kind and the total number of particles varies in time. The theory thus
extends the scope of the available and successful multiconfigurational
time-dependent Hartree methods -- which were solely formulated for and applied
to systems with a fixed number of particles -- to new physical systems and
problems. As a guiding example we treat explicitly a system where bosonic atoms
can combine to form bosonic molecules and vise versa. In the theory for
particle conversion, the time-dependent many-particle wavefunction is written
as a sum of configurations made of a different number of particles, and
assembled from sets of atomic and molecular orbitals. Both the expansion
coefficients and the orbitals forming the configurations are time-dependent
quantities that are fully determined according to the Dirac-Frenkel
time-dependent variational principle. Particular attention is paid to the
reduced density matrices of the many-particle wavefunction that appear in the
theory and enter the equations of motion. There are two kinds of reduced
density matrices: particle-conserving reduced density matrices which directly
only couple configurations with the same number of atoms and molecules, and
particle non-conserving reduced density matrices which couple configurations
with a different number of atoms and molecules. Closed-form and compact
equations of motion are derived for contact as well as general two-body
interactions, and their properties are analyzed and discussed.
