Evolution of Superoscillations in the Dirac Field

Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics (see [3, 12, 14, 26]) and in several other fields of science and technology, as it will be mentioned in the sequel. A natural problem, suggested by Aharonov, is to study the evolution of weak-values-superoscillations as initial datum of Schrödinger equation or as initial condition of other quantum field equations such are Klein–Gordon, see [10], or Dirac equation which is treated in this paper.