introduction-weak-interaction-volume-one

constants . Noninvariance of the weak Hamiltonian under the parity operato r
would imply that the weak interaction differentiates between differen t
directions in space, and hence that the multiplicative quantum numbe r
of intrinsic parity, which is assigned to all hadrons l , is not a 'good '
or conserved quantum number in the weak interactions . For the time
reversal operator :
I r
T (HI
(x, xo)) - E T Zi ( p (x' - xo) 0 . -Y'n (x, -x o ) ) X
where
X ( '( r e (_, - xo ) O i (C i + cl)r 5)-yv (x, -xo)) +
+ Hem . conj ., (3 .3 .21 )
E T = E T ( p ) . e- T (n) . 0 (e) E T (v) . (3 .3 .22 )
If the neutron decay Hamiltonian is to be invariant under T, then it mus t
act as a pure scalar under this transformation, so tha t
E T Ci =
6 T Cl '~ =
C i
(3 .3.23a )
Ci (3 .3 .23t )
With respect to the charge conjugation o p erator, the Hamiltonian behaves :
C ( HI (x, xo ) )
E C ~ i j (Zl n (x, x o ) Oi 3Vp (2 x o ) )
x
X
( v (-, x
o ) 0i ( ci + c! r 5 )'r (x, xo) ) +
+ Here . conj ., (3 .3 .24)
wher e
E C = F_c ( p ) . E c (n) . c(e) . 6 C (v) . (3 .3 .25 )
Thus we may deduce that C invariance demand s
G. * Ci = Ci (3 .3 .26a)
E C
C' = - Ci . (3 .3 .26b )
Finally, under the combined transformation CPT :
CPT (HI (x, x e )) = E c e p E T i 3(lir n (-x, - x o ) O i l r i ( -x, -xo )) X
~
X (-yry (-_,, -xo ) Oi (Ci - ci y 5 )1'Ie (-x, -x o )) i-
+ Helm . conj. (3 .3 .27)
1 . As we shall see in 3 .7, the weak. iamiltonian is indeed not invarian t
under the parity operator, and hence those particles which only take par t
in weak interactions have undefined parity . The photon's parity has see n
established as -1 by observing electromagnetic interactions .