Mathematical beauty behind particle production and Stokes phenomena

At the James Scott Prize Lecture in 1939, P. A. M. Dirac emphasized the theory of functions of a complex variable as an interesting mathematical theory that fulfilled his criteria of beauty. He found this field to be of “exceptional beauty” and hence likely to lead to deep physical insight [1]. The lecture was delivered a decade after he discovered the Dirac equation, the positron was found, and the concept of the Dirac sea was well established.

Dirac theory predicts that an external electric field may tilt the Dirac sea such that an electron in a negative energy…