Reduced integral representations for the probabilities of photon emission in a constant external electric field
DOI:
https://doi.org/10.33910/2687-153X-2022-3-4-167-175Keywords:
Photon emission, quantum electrodynamics, strong external field, Schwinger effect, Fourier transformationAbstract
In the case of an intense external electric field, there exist many transition channels corresponding to the violation of the vacuum stability. It was shown that depending on the setting of a problem there is a number of integral representations for the probabilities of one photon emission due to a constant electric field. These representations are the Fourier transformations of the product of two Weber parabolic cylinder functions that are solutions of the same differential equation. To simplify the study of the probabilities, we expressed such a Fourier transformation via the confluent hypergeometric function.
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