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Does a nonzero tunneling probability imply particle production in time-independent classical electromagnetic backgrounds?

Does a nonzero tunneling probability imply particle production in time-independent classical electromagnetic backgrounds?

In this paper, we probe the validity of the tunneling interpretation that is usually called forth in the literature to explain the phenomenon of particle production by time-independent classical electromagnetic backgrounds. We show that the imaginary part of the effective Lagrangian is zero for a complex scalar field quantized in …