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

Abstract

First, the case of (0 + 1)-dimensional nonequilibrium quantum mechanics is analyzed using the Yukawa model in external scalar field ${{\phi }_{{{\text{cl}}}}}(t) = \frac{m}{{{\lambda }}} + \frac{{{\alpha }}}{{{\lambda }}}t$ 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 $\phi$ 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.