On the Decay of a Strong Scalar Field in QM and QFT

First, the case of (0 + 1)-dimensional nonequilibrium quantum mechanics is analyzed using the Yukawa model in external scalar field as an example. It is shown that the exact fermion propagators do not change with time, and the growth of bosonic propagators is determined by the contribution to the quantum mean of field and corresponds to the so-called “tadpole” diagrams. After that, the Yukawa theory of the interacting massive Dirac field and massless real scalar field in the (1 + 1)-dimensional Minkowski space with the signature (+1, –1) is examined. In this theory, a classical current is first calculated, and then quantum corrections for the Dirac field in an external coordinate-dependent scalar field with Yukawa interaction are determined. The response of fermion pair generation to an external bosonic field that linearly depends on the coordinate is studied.