By Jeremy Bernstein

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T h e c h a r g e c o n j u g a t i o n c o n d i t i o n i s t h e s a m e as t h a t g i v e n a b o v e f o r t h e s p i n - z e r o case: c / , > ( o ) c - ' = -JAO), {a\J,y{0)\b) = W e m a y r e a d i l y define a p a r i t y t r a n s f o r m a t i o n o n t h e s p i n - l fields, 4/, t h a t guarantees that t h e vector t r a n s f o r m l i k e a proper L o r e n t z vector. Let'^ T h e n under this transformation'' 12. T h e e x t r a f a c t o r o f y t i n t h i s d e f i n i t i o n i s e s s e n t i a l , s i n c e \p{r, 1) a n d l A C - r , t) d o n o t o b e y the s a m e equation.

I t c a n b e s h o w n b y g r o u p - t h e o r e t i c a l m e t h o d s t h a t t h e r e a r e o n l y t w e l v e . H e r e w e u s e t h e "method" o f exhaustion. 1 1 . " 66 s t i l l f u r t h e r i n v a r i o u s cases o f i n t e r e s t . F r o m t h e H e r m i t i c i t y o f before {a\jy(0)\b} = Chapters w e h a v e , as Electron-Nucleon Scattering I: Form Factors C, P, T, and CPT 67 and P^ir, t)y4(r, {b\jyma)*, (a|7o^(0)|*) = Wo^ma)*. 74) T h u s 5 , t h e b a r y o n n u m b e r , is a t r u e scalar w h i l e / ; , ' ' , i n c l u d i n g b o t h t h e n u c l e o n s a n d p i o n s i s a t r u e v e c t o r .

10. S e e e s p e c i a l l y , J . J . S a k u r a i , A n n . , 1 1 : 1 ( 1 9 6 0 ) . T h e v e c t o r m e s o n s a r e d i s c u s s e d f u l l y i n C h a p t e r 14. 11. I t i s c o n v e n i e n t t o m e a s u r e t h e g r a v i t a t i o n a l c o n s t a n t i n u n i t s o f 1 / m ^ ' . T h u s G m i v " ~ I Q - ' " . 52 VB = Chapter 4 (4 50) T h i s is i d e n t i c a l i n a p p e a r a n c e t o t h e g r a v i t a t i o n a l p o t e n t i a l , so t h a t t h e p o t e n t i a l acting o n p w o u l d become, i n total.