4.3 Unified Field Model Based on PID and PRI
Equations (1.5.7) are the gauge covariant Dirac equations for all fermions participating
the four fundamental interactions. The left-hand sides of the field equations (1.5.3)-(1.5.6) are
the same as the classical Einstein equations and the standardU( 1 )×SU( 2 )×SU( 3 )gauge
field equations. The right-hand sides of are due to PID, and couple the four fundamental
interactions.
4.4.1 Duality
In the field equations (1.5.3)-(1.5.6), there exists a natural duality between the interaction
fields(gμ ν,Aμ,Wμa,Skμ)and their corresponding dual fields(φGμ,φe,φaw,φks). This duality
can be viewed as the duality between mediators and the duality between interacting forces,
summarized as follows:
(a)Duality of mediators.Each interaction mediator possesses a dual field
particle, called the dual mediator, and if the mediator has spin-k, then its
dual mediator has spin-(k− 1 ).(b)Duality of interacting forces.Each interaction generates both attracting
and repelling forces. Moreover, for each pair of dual fields,the even-spin
field generates an attracting force, and the odd-spin field generates a re-
pelling force.A few remarks are now in order.First, from the (phenomenological) weakton theory of elementary particles to be intro-
duced later, that each mediator and its corresponding dual mediator are the same type of
particles with the same constituents, but with different spins.
Second, from the duality of the mediators induced from the first principle PID, we con-
jecture that in addition to the neutral Higgs found by LHC in 2012, there must be two charged
massive spin−0 Higgs particles.
Third, the duality of interacting forces demonstrates thatall four forces can be both attrac-
tive and repulsive. For example, as the distance of two massive objects increases, the gravita-
tional force displays attraction as the Newtonian gravity,more attraction than the Newtonian
gravity in the galaxy scale, and repulsion in a much larger scale.
Fourth, as we shall see later, the 8 gluon fields produces repulsive force, and it is their
dual fields that produce the needed attraction for quark confinement. This gives a strong
observational evidence for the existence of the dual gluonsand for the valid and necessity of
PID.
Decoupling
The unified field model can be easily decoupled to study each individual interaction when
other interactions are negligible. In other words, PID is certainly applicable to each individual
interaction. For gravity, for example, PID offers to a new gravitational field model, leading
to a unified model for dark energy and dark matter as describedearlier in this introduction.