  The conventional, time-dependent Schroedinger equation describes only
unidirectional time evolution of the state of a physical system, i.e., forward
or, less commonly, backward. This paper proposes a generalized quantum dynamics
for the description of joint, and interactive, forward and backward time
evolution within a physical system. [...] Three applications are studied: (1) a
formal theory of collisions in terms of perturbation theory; (2) a
relativistically invariant quantum field theory for a system that kinematically
comprises the direct sum of two quantized real scalar fields, such that one
field evolves forward and the other backward in time, and such that there is
dynamical coupling between the subfields; (3) an argument that in the latter
field theory, the dynamics predicts that in a range of values of the coupling
constants, the expectation value of the vacuum energy of the universe is forced
to be zero to high accuracy. [...]
