... = r sin &+a6 z = rcosf?, and (11.226) 254 CONTINUOUS GROUPS AND REPRESENTATIONS Y’ Fig 11.6 (z,y,z) and the (z‘,y’,z‘) coordinates we obtain (Fig 11.6) L,= (11.227) d icotOsin 484 (11.2 28) (11.229) ... 11.133) (11.134) which induces infinitesimal as ( 11.136) Similarly, we write LORENTZ GROUP AND ITS LIE ALGEBRA 241 and (11.1 38) These give us the remaining generators as (11.139) and (11.140) Oi satisfy ... + L=?;’xT, (11. 188 ) by replacing position and momentum with their operator counterparts, that is, ?+?, (11. 189 ) as L = i - Px a‘ (11,190) Writing L in Cartesian coordinates we find its components...