Also notice, under parity p -p; or in spherical coordinates, ++ and -, the...

  

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Also notice, under parity p⇒ -p; or in spherical coordinates, Фр +Фр+п and Өр →П-Ор, the helicity eigenstates in equations (10.2.53) and (10.2.55) transform into each other: §+ → §¯¯ and §¯ → § +. (10.2.58) (10.2.59) Problem 10.28. Parity Matrix Show that the parity operator, defined as Pε = {¹, — takes the unique form - sin(0₂) e-i cos(p) eiop Cos (0p) - recall equations (10.2.58) and (10.2.59) P(0p, Op) = [ sin (6,))]. (10.2.66) (10.2.67) That this parity operator P depends on the angular parameters occurring within the $(0p, p) will turn out to be important for our SL2,c discussion below. In particular, it implies there is no P such that Poi P-1 = -oi . Also notice, under parity p⇒ -p; or in spherical coordinates, Фр +Фр+п and Өр →П-Ор, the helicity eigenstates in equations (10.2.53) and (10.2.55) transform into each other: §+ → §¯¯ and §¯ → § +. (10.2.58) (10.2.59) Problem 10.28. Parity Matrix Show that the parity operator, defined as Pε = {¹, — takes the unique form - sin(0₂) e-i cos(p) eiop Cos (0p) - recall equations (10.2.58) and (10.2.59) P(0p, Op) = [ sin (6,))]. (10.2.66) (10.2.67) That this parity operator P depends on the angular parameters occurring within the $(0p, p) will turn out to be important for our SL2,c discussion below. In particular, it implies there is no P such that Poi P-1 = -oi .