  While fundamental physically realistic Hamiltonians should be invariant under
time reversal, time asymmetric Hamiltonians can occur as mathematical
possibilities or effective Hamiltonians. Here, we study conditions under which
non-relativistic Hamiltonians involving particle creation and annihilation, as
come up in quantum field theory (QFT), are time asymmetric. It turns out that
the time reversal operator T can be more complicated than just complex
conjugation, which leads to the question which criteria determine the correct
action of time reversal. We use Bohmian trajectories for this purpose and show
that time reversal symmetry can be broken when charges are permitted to be
complex numbers, where `charge' means the coupling constant in a QFT that
governs the strength with which a fermion emits and absorbs bosons. We pay
particular attention to the technique for defining Hamiltonians with particle
creation based on interior-boundary conditions, and we find them to generically
be time asymmetric. Specifically, we show that time asymmetry for complex
charges occurs whenever not all charges have equal or opposite phase. We
further show that, in this case, the corresponding ground states can have
non-zero probability currents, and we determine the effective potential between
fermions of complex charge.
