Open Strings in Constant Electric and Magnetic Fields

Various properties of open strings in external constant E.M. fields are reviewed. In particular, the charged-particle pair production rate in an external electric field is evaluated, and shown to reduce to Schwinger’s formula in the limit of low-intensity fields. Open strings in external magnetic fields are shown to undergo an infinite number of phase transitions as the strenght of the field increases. 1. Open Strings in a Constant Electric-Field Background In the presence of an external constant electric field, quantum field theory predicts a nonvanishing probability for the creation of charged particle pairs. The rate of particle pair production can be estimated using simple semiclassical arguments. Namely, one represents a virtual charged particle pair in an external electric field of strenght E by a potential well of depth 2m, where m is the mass of the charged particle, superimposed to a linear potential V = 0, x < 0, V = 2m− eEx, x ≥ 0. (1) By denoting with e the charge of the particle and using the standard semi-classical approximation one would get a rate w ∼ exp(−O(1)m2/|eE|). This estimate is quite accurate. Indeed, the exact rate for a particle of spin s minimally coupled to an external electric field was found long ago by Schwinger: