18 CHAPTER 1. GENERAL INTRODUCTION
With the strong interaction potential (1.6.5), we can calculate the strong interaction bound
energyEfor two same type of particles:
(1.6.7) E=g^2 s(ρ)
[
1
r−
A
ρ( 1 +kr)e−kr]
.
The quark confinement can be well explained from the viewpoint of the strong quark
bound energyEqand the nucleon bound energyEn. In fact, by (1.6.7) we can show that
(1.6.8) Eq= 1020 En∼ 1018 GeV.
This clearly shows that the quarks is confined in hadrons, andno free quarks can be found.
4.5.7 Short-range nature of strong interaction
Asymptotic freedom was discovered and described by (Gross and Wilczek, 1973 ;Politzer,
1973 ). Using the strong interaction potential (1.6.5), we can clearly demonstrate the asymp-
totic freedom property and the short-ranged nature of the strong interaction.
1.7 Theory of Weak Interactions
The new weak interaction theory based on PID and PRI was first discovered by (Ma and Wang,
2013a). As addressed earlier, the weak interaction obeys theSU( 2 )gauge symmetry, which
dictates the standardSU( 2 )Yang-Mills action. By PID and PRI, the field equations of the
weak interaction are given by:
Gabw[
∂μWμ νb −gwλcdbgα βWα νcWβd]
−gwψwγνσaψw=[
∂μ+γb^1 Wμb−1
4
m^2 wxμ]
(1.7.1) φaw,
(1.7.2) (iγμDμ−ml)ψw= 0.
1.Higgs fields from first principles.The right-hand side of (1.7.1) is due to PID, leading
naturally to the introduction of three scalar dual fields. The left-hand side of (1.7.1) represents
the intermediate vector bosonsW±andZ, and the dual fields represent two charged Higgs
H±(to be discovered) and the neutral HiggsH^0 , with the later being discovered by LHC in
2012.
It is worth mentioning that the right-hand side of (1.7.1), involving the Higgs fields, can
not be generated by directly adding certain terms in the Lagrangian action, as in the case for
the new gravitational field equations derived in (Ma and Wang,2014e).
2.Duality.We establish a natural duality between weak gauge fields{Wμa}, representing
theW±andZintermediate vector bosons, and three bosonic scalar fieldsφaw, representing
both two charged and one neutral Higgs particlesH±,H^0.
3.Spontaneous gauge symmetry-breaking.PID induces naturally spontaneous symmetry
breaking mechanism. By construction, it is clear that the Lagrangian actionLWobeys the
SU( 2 )gauge symmetry, the PRI and the Lorentz invariance. Both theLorentz invariance
and PRI are universal principles, and, consequently, the field equations (1.7.1) and (1.7.2)