288 CHAPTER 5. ELEMENTARY PARTICLES
3) Mediator decay:2 γ→e++e−,
(5.3.3) W±→l±+νl±,
Z→l++l−,wherel±are the charged leptons.All leptons, quarks and mediators are currently regarded aselementary particles. How-
ever, the decays in (5.3.1)-(5.3.3) show that these particles must have an interior structure,
and consequently they should be considered as composite particles rather than elementary
particles:5.3.1 Decay means the interior structure.
5.3.2 Theoretical foundations for the weakton model
Subatomic decays and electron radiations indicate that there must be interior structure for
charged leptons, quarks and mediators. The main objective of this section is to propose an
elementary particle model, which we call weakton model, based on the weak and strong
interaction theories developed in the last chapter.6.2.4 Angular momentum rule
It is known that the dynamic behavior of a particle is described by the Dirac equations:(5.3.4) ih ̄∂ ψ
∂t=Hψ,whereψ= (ψ 1 ,ψ 2 ,ψ 3 ,ψ 4 )Tis the Dirac spinor,His the Hamiltonian:(5.3.5) H=−i ̄hc(αk∂k)+mc^2 α^0 +V(x),Vis the potential energy,αk( 1 ≤k≤ 3 )are the matrices as given by (2.2.48), andα^0 is the
matrix as
α^0 =
(
I 0
0 −I
)
, I=
(
1 0
0 1
)
.
By the conservation laws in quantum mechanics, if an Hermitian operatorLcommutes with
Hin (5.3.5):
LH=HL,
then the physical quantityLis conserved.
Consider the total angular momentum~Jof a particle as~J=~L+s~S,where~Lis the orbital angular momentum~L=~r×~p, ~p=−i ̄h∇,