196 CHAPTER 4. UNIFIED FIELD THEORY
4.2.3 Higgs mechanism and mass generation
Principle4.4of gauge symmetry breaking is also a main motivation to postulate PID in our
program for a unified field theory. In fact, the Higgs mechanism is one way to achieve
the spontaneous gauge-symmetry breaking. In the Glashow-Weinberg-Salam (GWS) elec-
troweak theory, the three intermediate vector bosonsW±andZfor the weak interaction re-
tain their masses by the Higgs mechanism. We now show that themasses of the intermediate
vector bosons can be also obtained by PID. Furthermore, we shall show in Section4.6that
all conclusions of the GWS electroweak theory confirmed by experiments can be derived by
the unified field theory based on PID.
For convenience, we first introduce some related basic knowledge of quantum physics.
In quantum field theory, a fieldψis called a fermion with massm, if it satisfies the Dirac
equation
(4.2.17) (iγμDμ−m)ψ= 0 ,
and the action of (4.2.17) is
(4.2.18) LF=
∫
LFdx, LF=ψ(iγμDμ−m)ψ,whereψ=ψ†γ^0.
A fieldΦis called a boson with massm, ifΦsatisfies a Klein-Gordon type of wave
equation:
(4.2.19) Φ+
(mc
h ̄) 2
Φ=g(Φ),whereg(Φ)is the terms ofΦother thankΦ(ka constant), andis the wave operator given
by
=−∂μ∂μ=1
c^2∂^2
∂t^2−∆.
The bosonic fieldΦis massless if it satisfies
(4.2.20) Φ=g(Φ).
The physical significances of the fermionic and bosonic fieldsψandΦare as follows:1) Macro-scale:ψandΦrepresent field energy density. In particular, ifΦis a gauge field
then it stands for the interaction potential correspondingto the gauge theory.2) Micro-scale (Quantization):ψrepresents a spin-^12 fermionic particle, andΦrepresents
a bosonic particle with an integer spinkifΦis ak-th order tensor field.In particular, in the classical Yang-Mills theory, theSU(N)gauge fieldsAaμ= (Aa 0 ,Aa 1 ,Aa 2 ,Aa 3 )( 1 ≤a≤N^2 − 1 )satisfy the following field equations:
(4.2.21) ∂μFμ νa =o(Aμ), Fμ νa =∂μAaν−∂νAaμ+gλbcaAbμAcν,