Schwinger pair production via instantons in strong electric fields

Abstract

In the space-dependent gauge, each mode of the Klein-Gordon equation in a strong electric field takes the form of a time-independent Schrödinger equation with a potential barrier. We propose that the single-and multi-instantons of quantum tunnelling may be related with the single-and multi-pair production of bosons and the relative probability for the no-pair production is determined by the total tunnelling probability via instantons. In the case of a static uniform electric field, the instanton interpretation recovers exactly the well-known pair production rate for bosons and when the Pauli blocking is taken into account, it gives the correct fermion production rate. The instanton is used to calculate the pair-production rate even in an inhomogeneous electric field. Furthermore, the instanton interpretation confirms the fact that bosons and fermions cannot be produced by a static magnetic field only.

World-line instantons and the Schwinger effect as a Wentzel–Kramers–Brillouin exact path integral

“…(−1) (n+1) E 2 8π 3 n 2 e −πm 2 n/|E| (2) Here m is the mass of the particles, V is the space-time volume and E is the electric field. We have absorbed a factor of the particle charge into E. The result (2) is obtained by evaluating the vacuum persistence amplitude in a theory with a charged massive scalar field exposed to an external electric field.…”

Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields

“…Let us start with a brief review of the world-line instanton method, see, e.g., [52][53][54][55][56][57][58][59][60]. Since the electron spin does not affect the exponent of the pair creation probability [55], we consider the vacuum persistence amplitude of scalar QED…”

“…1 In the following, we venture a first step into this direction and employ the worldline instanton technique (see, e.g., [52][53][54][55][56][57][58][59][60]) in order to study the superposition of a spatial and a temporal field pulse as an example for a genuinely space-time dependent field.…”

Critical Schwinger Pair Production

“…This sets a dual example as the phenomenon of pair production in strong external fields can be derived from the Dirac equation which -despite its quantum mechanical interpretation -can be viewed as a classical deterministic field equation. In fact, the first observation of this phenomenon relied on this formulation [5], and so do many more modern approaches at least indirectly [6][7][8][9][10][11]. On the other hand Schwinger pair production is also encoded in the photon correlation functions derived from the full functional integral of QED, as seen from the derivations of Euler, Heisenberg [12], and Schwinger [13].…”

“…The worldline action (6) cannot become singular in this case, so the scaling law is solely determined by the fluctuation prefactor and thus by the way in which f ′ (u) approaches zero for u → u 0 , cf. (8). Let us assume that the electric field drops to zero as E(x) ∼ (u 0 /k − x) n .…”