introduction-weak-interaction-volume-one

e
and
c = m .
0
(1 .7 .15 )
(1 .7 .16 )
The commutation relation (1 .7 .14) implies that 1 is not a number, since i t
does not commute, but no unique solution is possible, since (1 .7 .14) is the
only defining relation .
4
is usually identified with the set of 4 X 4
Dirac-Pauli (37) matrices, define d
0 - j 6
k (k - 1 ;2,3 )
J ' k 0
(1 .7 .17 )
Y4=
0 -1 _
each element standing for a 2 X 2 matrix . t5K are the Pauli spin matrices :
r_
(S1 _ 0 c _ I-o
1 o
1 0
0 d 3 -1
(1 .7 .18 )
and
Li
1 = r l 0 o [o 0
(1 .7 .19 )
L 0 Lo 0
The multiplication of the Y matrices among themselves yields sixtee n
further independent matrices :
product
number of matrices,
1 (unit matrix) 1
1/ r
ar ds (r < s)
Yr (s ~t
(r K s Kt )
y l Y2Y3 ( = Y 5 ) (4
0
4
6
4
1
It is useful also to define a matrix Y 5
0 -1
y-2
,
Y 5
-1 0
(1 .7 .20)