introduction-weak-interaction-volume-one

in two parts (1) :
t ) = 2t
(2 .1 .9 )
H(x) = oc p+Y4
m + v(x) = -ix, (a /a k) t't 4m + V(x) (2 .1 .10 )
We assume a similar symmetry for the potential V(x) as (2 .1 .5) for the Hamiltonian ,
and writ e
V(-x) = V(x) , (2 .1 .11 )
Using the anticommutation relations of the
matrices, we obtain the propert y
H(-x) _ 4 H(x) Y4
(2 .1 .12 )
for the Hamiltonian in (2 .1 .10) . Applying the P operator and using (2 .1 .12) ,
(2 .1 .9) become s
H(x) t) j ( x ,t) (2 .1 .13
v4 -
)
Y4
Introducing
y' (x, t )
(2 .1 .14 )
'(4(-, t )
and multiplying by y4, (2 .1 .13) simplifies t o
(2 .1 .15)
H(x) .1J' (x, t ) = ~ZI~ ~(x 4 t )
a t
(2 .1 .15) is identical with the original equation (2 .1 .9), and hence thi s
equation is invariant under the P operator, implying that in all physical processe s
which are describable by the Dirac
parity is conserved .
equation, the quantum number of intrinsi c
The charge conjugation operator, C, transforms a given particle into it s
antiparticle . From similar considerations as those which we employed fo r
parity, we may see that many physical systems will have a definite
eigenvalue
with respect to the C operator, or C parity . Symmetry under the C operato r
in classical physics is shown by the invariance of Maxwell's equations under
a change in the sign of the charge and current densities . Only a few particle s
have even C parity, since all baryons (nucleons and hyperons) have B z 1 ,
while antibaryons have B and similarly leptons have L 1, whereas
antileptons have L - -1 . Since both baryon number, B, and lepton number, L ,
are thought to be conserved in all reactions, no baryon or lepton may ever
commute with its antiparticle .
The only stable particles with neither charg e
nor lepton or baryon number are the photon, the m, and the K°. Of these, onl y
the IT° has even C parityl (2) .