introduction-weak-interaction-volume-one

`,{ r (a/axr ) J(x) = ( Y i ('a /a x.) + r 4 (2/3 x4 ) x) = 0 (2 .5 .14 )
Multiplying through by
Y4 and using the '( matrix properties, we obtai n
(j Y 5 Si ( /a xi ) + ('O/a x4 ) y(x) = 0 . (2 .5,15 )
If we choose a representation such as the one discussed earlier for
f5 so tha t
it is diagonalized i .e . all its nonzero components lie on its leading diagonal ,
and then write our field W(x) in terms of it, we hav e
't' (x) = +(I +Y5)y'(x)
a
+
z(1 - Y5)v(x )
(x) (x) . (2 .5 .16 )
(2 .5 .15) now resolves into two uncoupled relation s
(J6, (a/ax) -f- (a/ax4 ) cx (x) = 0 (2 .5 .17 )
(—J6 r(~ /a xr) + ( / a x4)
l
(x) = 0 . (2 .5 .18 )
(2 .5 .17) and (2 .5 .18) are known as the Weyl equations for massless spin 1
particles, and which describe the neutrinos . The spinors 0((x) and (x )
have only two components each, and hence the matrices 6r are 2 X 2 matrices .
These are usually identified with the Pauli spin matrices (1 .7 .18) .
We find that
the massless spinor if(x) may be represented, according to the Weyl equations (13 )
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