2001/11/15 by A. I. Nikishov, Nikishov, A. I.
Engineering · Materials Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Laser-induced spectroscopy and plasma #Solidification and crystal growth phenomena #Statistical Mechanics and Entropy #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0111137
19 pages, LATEX2e, no figures, some typos corrected, some additions
openalex publication_date 2001/11/15 · arxiv created 2003/01/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of the scalar pair production by a one-dimensional vector- potential Aμ(x3) is reduced to the S- matrix formalism of the theory with an unstable vacuum. Our choice of in- and out-states does not coincide with that of other authors and we argue extensively in favor of our choice. In terms of our classification the states that can be created by the field enter into the field operator in the same way as do the states that cannot be created by the field, i.e. the field operator has the usual form. We show that the norm of a solution of the wave equation is determined by one of the amplitude of its asymptotic form for x3→ ±∞. For the step potential and for the constant field potential we get the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. For the constant electric field we obtain the scalar particle propagator in terms of the stationary states and show that with our choice of in- and out-states it has the form dictated by the general theory.