On the Strong Scalar Field Decay in QM and QFT

   First, the case of (0 + 1)-dimensional nonequilibrium quantum mechanics is considered by solving the Yukawa model in an external scalar field φcl (t) = m/L+a/L*t. 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 average of the field and corresponds to the so-called “tadpole” diagrams. Then, the Yukawa theory of the interacting massive Dirac field and the massless real scalar field in the (1 + 1)-dimensional Minkowski space with the signature (+1, –1) is considered. In this theory we first calculate a classical current, and then quantum corrections for the Dirac field in an external coordinate-dependent scalar field with Yukawa interaction. We study the response of the production of fermion pairs to an external bosonic field linearly dependent on the coordinate.

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