  Particles and fields are standard components in numerical simulations like
transport simulations in nuclear physics and have very well understood
dynamics. Still, a common problem is the interaction between particles and
fields due to their different formal description. Particle interactions are
discrete, point-like events while fields have purely continuous equations of
motion. A workaround is the use of effective theories like the Langevin
equation with the drawback of energy conservation violation. We present a new
method, which allows to model non-continuous interactions between particles and
scalar fields, allowing us to simulate scattering-like interactions which
exchange energy and momentum quanta between fields and particles obeying full
energy and momentum conservation and control over interaction strengths and
times. In this paper we apply this method to different model systems, starting
with a simple scalar harmonic oscillator which is damped by losing discrete
energy quanta. The second and third system is a scalar oscillator and a one
dimensional field which are both damped by discrete energy loss and which are
coupled to a stochastic force, leading to equilibrium states which correspond
to statistical Langevin-like systems. The last example is a scalar field in 3D
which is coupled to a microcanonical ensemble of particles by incorporating
particle production and annihilation processes. Obeying the detailed-balance
principle, the system equilibrates to thermal and chemical equilibrium with
dynamical fluctuations on the fields, generated dynamically by the discrete
interactions.
