von ▁Ne umann ▁theorem ▁gives ▁a ▁uniqu eness ▁result ▁for ▁operators ▁satisfying ▁( an ▁exponent i ated ▁form ▁of ) ▁the ▁canonical ▁commut ation ▁relation . ▁ ▁Rel ation ▁to ▁classical ▁mechan ics ▁ ▁By ▁contrast , ▁in ▁classical ▁physics , ▁all ▁observ ables ▁comm ute ▁and ▁the ▁commut ator ▁would ▁be ▁zero . ▁However , ▁an ▁analog ous ▁relation ▁exists , ▁which ▁is ▁obtained ▁by ▁replacing ▁the ▁commut ator ▁with ▁the ▁Po isson ▁bra cket ▁multip lied ▁by ▁: ▁ ▁This ▁observation ▁led ▁Di rac ▁to ▁propose ▁that ▁the ▁quantum ▁counter parts ▁▁ ▁, ▁▁ ▁of ▁classical ▁observ ables ▁, ▁ ▁satisfy ▁ ▁In ▁ 1 9 4 6 , ▁H ip ▁Gro en ew old ▁demonstrated ▁that ▁a ▁general ▁system atic ▁correspond ence ▁between ▁quantum ▁commut ators ▁and ▁Po isson ▁brackets ▁could ▁not ▁hold ▁consist ently . ▁However , ▁he ▁did ▁appreciate ▁that ▁such ▁a ▁system atic ▁correspond ence ▁does , ▁in ▁fact , ▁exist ▁between ▁the ▁quantum ▁commut ator ▁and ▁a ▁de formation ▁of ▁the ▁Po isson ▁bra cket , ▁the ▁Mo yal ▁bra cket , ▁and , ▁in ▁general , ▁quantum ▁operators ▁and ▁ ▁classical ▁observ ables ▁and ▁distributions ▁in ▁phase ▁space . ▁He ▁thus ▁finally ▁el uc id ated ▁the ▁correspond ence ▁mechanism , ▁the ▁W igner – W ey l ▁transform , ▁that ▁under lies ▁an ▁alternate ▁equivalent ▁mathematical ▁representation ▁of ▁quantum ▁mechan ics ▁known ▁as ▁de formation ▁quant ization . ▁ ▁The ▁W ey l ▁relations ▁ ▁The ▁group ▁ ▁generated ▁by ▁exponent iation ▁of ▁the