4.1 Principles of Unified Field Theory
2) the coupling of the four interactions is achieved through PID and PRI in
the unified field equations, which obey the PGR and PRI, but break sponta-
neously the gauge symmetry.In this chapter, there are four sections. Section4.1presents the general view of the uni-
fied field theory, the geometry of unified fields, gauge-symmetry breaking, PID, and PRI.
Section4.2presents the experimental and observational physical supports for PID. The math-
ematical reason from the well-posedness point of view is also given. Section4.3introduces
4.3.1 Unified field equations based on PID.
tion4.4presents the natural duality between the gauge fields and their dual fields, as well as
the decoupling of the unified field equations to the field equations for individual interaction
when the other interactions are negligible.
4.1 Principles of Unified Field Theory
4.1.1 Four interactions and their interaction mechanism
The four fundamental interactions/forces of Nature include
1) the gravitational force, generated by the mass chargeM, which is responsible to all
macroscopic motions,2) the electromagnetic force, generated by the electric chargee, which holds the atoms
and molecules together,3) the strong force, generated by the strong chargegs, which mainly acts at three levels:
quarks and gluons, hadrons, and nucleons, and4) the weak force, generated by the weak chargegw, which provides the binding energy
to hold the mediators, the leptons and quarks together.The most crucial ingredient of each interaction is its corresponding interaction potential
Φand chargeg. The relation between the corresponding forceF, its associated potentialΦ
and its chargegis as follows:
(4.1.1) F=−g∇Φ,
where∇is the three-dimensional spatial gradient operator. The chargegfor each interaction
is given as follows:
(4.1.2)
m the mass charge for gravity,
e the electric charge for electromagnetism,
gs the strong charge for strong interaction, and
gw the weak charge for the weak interaction.