Square-root operator quantization and nonlocality: A review (Q5955526)

This is a review on methods how to deal with operators depending nonlinearly on an operator, the main example being the quantization of the relativistic energy operator \[ E=\sqrt {m^2+p^2}. \] Quantization means that the momentum \(p\) is replaced by \(i\) times the gradient operator, so \[ \widehat E=\sqrt {m^2-\square}. \] Applications are the scalar particle, the Higgs particle and electromagnetism. Methods are the Fourier transforms, transformation to integral equations, and Green's functions. Locality and causality are thoroughly discussed.