▁in var iance ▁Can on ical ▁quant ization ▁is ▁applied , ▁by ▁definition , ▁on ▁canonical ▁coordinates . ▁ ▁However , ▁in ▁the ▁presence ▁of ▁an ▁elect romagnet ic ▁field , ▁the ▁canonical ▁momentum ▁ ▁is ▁not ▁gauge ▁invariant . ▁ ▁The ▁correct ▁gauge - in variant ▁momentum ▁( or ▁" kin etic ▁momentum ") ▁is ▁▁ ▁  ▁( SI ▁units ) ▁      ▁ ▁  ▁( c gs ▁units ), ▁ ▁where ▁ ▁is ▁the ▁particle ' s ▁electric ▁charge , ▁ ▁is ▁the ▁vector ▁potential , ▁and ▁ ▁is ▁the ▁speed ▁of ▁light . ▁Although ▁the ▁quantity ▁ ▁is ▁the ▁" phys ical ▁momentum ", ▁in ▁that ▁it ▁is ▁the ▁quantity ▁to ▁be ▁identified ▁with ▁momentum ▁in ▁labor atory ▁experiments , ▁it ▁does ▁not ▁satisfy ▁the ▁canonical ▁commut ation ▁relations ; ▁only ▁the ▁canonical ▁momentum ▁does ▁that . ▁This ▁can ▁be ▁seen ▁as ▁follows . ▁ ▁The ▁non - rel ativ istic ▁Hamiltonian ▁for ▁a ▁quant ized ▁charged ▁particle ▁of ▁mass ▁ ▁in ▁a ▁classical ▁elect romagnet ic ▁field ▁is ▁( in ▁c gs ▁units ) ▁ ▁where ▁ ▁is ▁the ▁three - vector ▁potential ▁and ▁▁ ▁is ▁the ▁scalar ▁potential . ▁This ▁form ▁of ▁the ▁Hamiltonian , ▁as ▁well ▁as ▁the ▁Sch r öd inger ▁equation ▁ ▁, ▁the ▁Max well ▁equations ▁and ▁the ▁Lor ent z ▁force ▁law ▁are ▁invariant ▁under ▁the ▁gauge ▁transformation ▁ ▁where ▁ ▁and ▁ Λ = Λ ( x , t ) ▁is ▁the ▁gauge ▁function . ▁ ▁The ▁angular ▁momentum ▁operator ▁is ▁▁