The PZW transformation operator can also be expressed as Û = exp -i h 2ω c /h μA 0 Qc = expi h ( j z j Âx j ) . Recall that a momentum boost operator Ûp = e -i h p 0 q boosts p by the amount of p 0 , such that Ûp Ô(p) Û † p = Ô(p + p 0 ). Hence, Û simultaneously boosts the photonic momentum pc by 2ω c /h μA 0 and the matter momentum Pj by z j Â. Using Û † to boost the matter momentum, one can show that