Exactly solvable cases in QED with t-electric potential steps

Abstract: In this paper, we present in detail consistent QED (and scalar QED) calculations of particle creation effects in external electromagnetic field that correspond to three most important exactly solvable cases of t-electric potential steps: Sauter-like electric field, T-constant electric field, and exponentially growing and decaying electric fields. In all these cases, we succeeded to obtain new results, such as calculations in modified configurations of the above mentioned steps and detailed considerations of new limiting cases in already studied before steps. As was recently discovered by us, the information derived from considerations of exactly solvable cases allows one to make some general conclusions about quantum effects in fields for which no closed form solutions of the Dirac (or Klein-Gordon) equation are known. In the present article we briefly represent such conclusions about an universal behavior of vacuum mean values in slowly varying strong electric fields.