Generalized two-point tree-level amplitude $jf\to j^{\mathrm{\prime }}{f}^{\mathrm{\prime }}$ in a magnetized medium

The tree-level two-point amplitudes for the transitions $jf \to j^{, \prime} f^{, \prime}$,where$f$isafermionand$j$ is a generalized current, in a constant uniform magnetic field of an arbitrary strength and in charged fermion plasma, for the $jff$ interaction vertices of the scalar, pseudoscalar, vector and axial-vector types have been calculated. The generalized current $j$ could mean the field operator of a boson, or a current consisting of fermions, e.g. the neutrino current. The particular cases of a very strong magnetic field, and of the coherent scattering off the real fermions without change of their states (the “forward” scattering) have been analysed. The contribution of the neutrino photoproduction process, $\gamma e\to e\nu \bar{\nu }$, to the neutrino emissivity has been calculated with taking account of a possible resonance on the virtual electron.