Geodesic
On the production of $e^+e^-$-pairs from the vacuum under the influence of an electric field
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 34-46

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A study is made of the problem of pair production of particies with spin $1/2$ in an external homogeneous electric field $\mathbf E(t)$. The Heisenberg equations of motion are found for the operators of creation and annihilation, a solution for which has the form of a linear canonical transformation. A system of differential equations that determine the coefficients $U(t)$ and $V(t)$ of this transformation are obtained. The probabilities of pair creation are expressed in terms of the eigenvalues of the matrix $VV^+$. The ease of particles with anomalous magnetic moment is also considered. 
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     author = {M. S. Marinov and V. S. Popov},
     title = {On the production of $e^+e^-$-pairs from the vacuum under the influence of an electric field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {1973},
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M. S. Marinov; V. S. Popov. On the production of $e^+e^-$-pairs from the vacuum under the influence of an electric field. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 34-46. http://geodesic.mathdoc.fr/item/TMF_1973_17_1_a3/