asc ual ▁Jordan ▁in ▁ 1 9 3 5 ▁and ▁was ▁util ized ▁by ▁Julian ▁Schw inger ▁ ▁in ▁ 1 9 5 2 ▁to ▁re - work ▁out ▁the ▁theory ▁of ▁quantum ▁angular ▁momentum ▁efficiently , ▁given ▁that ▁map ’ s ▁ease ▁of ▁organ izing ▁the ▁( sym metric ) ▁representations ▁of ▁ ▁su ( 2 ) ▁in ▁F ock ▁space . ▁ ▁The ▁map ▁util izes ▁several ▁creation ▁and ▁anni h ilation ▁operators ▁▁▁ ▁and ▁ ▁of ▁routine ▁use ▁in ▁quantum ▁field ▁theories ▁and ▁many - body ▁problems , ▁each ▁pair ▁representing ▁a ▁quantum ▁harm onic ▁oscill ator . ▁The ▁commut ation ▁relations ▁of ▁creation ▁and ▁anni h ilation ▁operators ▁in ▁a ▁multiple - bos on ▁system ▁are , ▁▁▁▁ ▁where ▁ ▁is ▁the ▁commut ator ▁and ▁ ▁is ▁the ▁Kr one cker ▁delta . ▁ ▁These ▁operators ▁change ▁the ▁eigenvalues ▁of ▁the ▁number ▁operator , ▁ ▁, ▁by ▁one , ▁as ▁for ▁mult id im ensional ▁ ▁quantum ▁ ▁harm onic ▁oscill ators . ▁ ▁The ▁Jordan ▁map ▁from ▁a ▁set ▁of ▁matrices ▁ ▁to ▁F ock ▁space ▁bil ine ar ▁operators ▁, ▁▁▁ ▁is ▁clearly ▁a ▁Lie ▁Al gebra ▁isomorphism , ▁i . e . ▁the ▁operators ▁ ▁satisfy ▁the ▁same ▁commut ation ▁relations ▁as ▁ ▁the ▁matrices ▁. ▁ ▁For ▁example , ▁ ▁the ▁image ▁of ▁the ▁ ▁Paul i ▁matrices ▁of ▁SU ( 2 ) ▁in ▁this ▁map , ▁▁▁▁ ▁for ▁two - vector ▁a † s , ▁and ▁as ▁satisfy ▁the ▁same ▁commut ation ▁relations ▁of