One-loop amplitude of the transition j→f(f)over-bar→j′ in an external electromagnetic field

The external-field-induced one-loop contributions to the generalized amplitude for the transition j --> f (f) over bar --> j' have been calculated for a constant uniform magnetic field and for a crossed field. The results obtained for arbitrary combinations of the scalar, pseudoscalar, vector, and pseudovector interactions of currents with fermions can be widely used, together with the mass operators for scalar and pseudoscalar particles and the photon polarization operator in an external electromagnetic field, to analyze various transitions in a magnetic or in a crossed field, such as the decay processes nu --> nu gamma, nu --> nu e(-)e(+), a --> nu<(nu)over bar>, and a --> e(-)e(+) and axion-photon oscillations.