Recall that a momentum boost operator Ûp = e -i ℏ p0 q displaces p by the amount of p 0 , such that Ûp Ô(p) Û † p = Ô(p + p 0 ). Hence, Û is a boost operator for both the photonic momentum pc by the amount of 2ω c /ℏ μA 0 , as well as for the matter momentum pj by the amount of z j Â. The PZW gauge operator (Eq. 48) is a special case of Ûχ , such that χ = -x j • Â, where χ now also explicitly dependents on Â (as appose to a pure function of matter coordinates).