Composite worldline instantons and the nonperturbative particle decay in constant external electric and magnetic fields

Abstract

In this paper, we discuss the validity of the composite worldline instanton approach for the nonperturbative decay of charged particles in constant electric and magnetic fields. It is shown that the instanton results in the leading exponential approximation in the different limits agree with the ones obtained by the imaginary part of the self-energy in the external field and by overlap of the wave functions. We comment on the possible application of our results for the estimation of the decay rate of the proton in the external electric and magnetic field in the leading exponential approximation. The effects of entanglement of the particles in the final state are briefly mentioned.