ON THE INTERPRETATION OF THE SCHWINGER AND LANDAU-ZENER EFFECTS

The dynamical mechanism of the Schwinger effect of vacuum pair creation (VPC) under action of a strong external electric field is discussed. It is shown that the common interpretation of this process as the tunnelling between states with negative and positive energies is not universal and depends on the choice of electromagnetic field gauge. We discuss the mechanism of VPC based on the growth of virtual vacuum fluctuations (zitterbewegung). Finally, we consider the parallels between the Schwinger effect in QED and the Landau-Zener effect in solid state physics. 1. The original idea [1] about vacuum pair creation (VPC) under action of a stationary spatially homogeneous electric field was based on the model of particle tunnelling between the states with negative and positive energy in the Dirac model of physical vacuum. The authors turn your attention to the obvious picture that the electric field with the 4-potential A0(x) = φ(x) = −Ex3, A(x, t) = 0 (1) leads to appearance of a potential barrier between the two regions with the dispersion laws (cf. Fig.1) ω±pot(p,x) = eφ(x) ± ω0(p), (2) where ω0 = m2 + p2 (below we concentrate on the case of QED as the basic quantum field model), e is the electron charge with its sign, E is the electric field strength oriented along of the axes x3). This model results in the exponential factor exp(−Ec/E) for the tunneling probabilibty, with the critical field Ec = m2/e (here and below we use the natural units ~ = c = 1). This result was confirmed and generalized by J. Schwinger [2] who obtained the well-known exact solution of the corresponding QED problem: w = 1