Elementary Particle Physics by Stephen Gasiorowicz

By Stephen Gasiorowicz

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4 8 , 5 6 8 ( 1 9 4 7 ) , a n d R . F . S t r e a t e r a n d A . S . W i g h t m a n , P C T , Spin Statistics and A l l T h a t , W . A . B e n j a m i n , N e w Y o r k ( 1 9 6 4 ) . I n a l l o f t h e s e p a p e r s a n u m b e r o f subtle points, which w e gloss over, a r e discussed. A m o n g t h e m a r e t h e distinction between t h eg r o u p o f L o r e n t z transformations a n d t h e"covering g r o u p " o f 2 x 2 complex matrices, which is really t h eo n e being studied. A detailed coverage o f these matters w o u l d take u p a prohibitive a m o u n t o f space a n d w o u l d n o ta d d a n y t h i n g to o u r understanding o f the basic physical consequences o f Lorentz invariance discussed in this chapter.

1 1 2 , 6 6 9 ( 1 9 5 8 ) ; K . N i s h i j i m a , Phys. Rev. I l l , 9 9 5 ( 1 9 5 8 ) ; W . Z i m m e r m a n n , Nuovo. Cimento, 1 0 , 59 ( 1 9 5 8 ) . ^ A l m o s t allo f the material contained i n this chapter appears explicitly o r implicitly i n t h e p i o n e e r i n g p a p e r o f E . P . W i g n e r , A n n . M a t h . 4 0 , 1 4 9 (1939). S e e a l s o V . B a r g m a n n , and A n n . M a t h . 4 8 , 5 6 8 ( 1 9 4 7 ) , a n d R . F . S t r e a t e r a n d A . S . W i g h t m a n , P C T , Spin Statistics and A l l T h a t , W .

57) w h e r e »7 i s a p h a s e f a c t o r a n d A i s s o m e m a t r i x t o b e d e t e r m i n e d s o t h a t t h e e q u a t i o n i s f o r m - i n v a r i a n t . 53) reduces, after a little algebra, t o the c o n d i t i o n (2:''\y'']= - / W - g V ) 39 A n important byproduct o f this is that t h e transformation o f bilinear c o m b i n a t i o n s can easily b e f o u n d . 75)]. ^S"^ Field a;,. 59) w h i c h s h o w s t h e c o n n e c t i o n b e t w e e n t h e a^, a n d t h e p a r a m e t e r s c h a r a c terizing the rotation.

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