4.1. PRINCIPLES OF UNIFIED FIELD THEORY 185
First, the unified field model of (4.1.14) and (4.1.15) not only solves the most basic prob-
lems 1)-10) mentioned above, but also is the simplest with respect to the underlying physical
principles and to the explicit form of the field equations coupling four forces.
Second, the new unified field theory based on PID, PRI and PSB addressed in this chapter
offers an answer to dark energy and dark matter problem; see also Section7.6.3.
Third, thanks to PRI, we have shown that the classicalSU( 3 )Yang-Mills theory will
only provide a repulsive force. The attractive bounding force between quarks are due to the
dual fields in the PID-inducedSU( 3 )gauge theory. In other words, the quark confinement
problem is solved in (Ma and Wang,2014c), and will be addressed in detail in Section4.5.3.
Also, the route of unification (4.1.14) and (4.1.15) is readily applied to multi-particle
interacting systems, and gives rise to a first dynamic interacting model for multi-particle
systems; see Chapter 6 for details.
Finally, we present a diagram to illustrate the framework ofthe unified field theory, based
on (4.1.14) and (4.1.15). We note that quantization is used mainly for deriving transition
probability from the field equations for each interaction.
Unified Field Model4.4.4 Strong interaction field equations
Interaction Potentials5.5 Structure of Mediator Clouds Around Subatomic Particles
6.4 Energy Levels of Subatomic Particles
decouplingsolutions4.1.3 Geometry of unified fields
Hereafter we always assume that the space-time manifoldMof our Universe is a 4-dimensional
Riemannian manifold. We adopt the view that symmetry principles determine the geometric
structure ofM, and the geometries ofMassociated with the fundamental interactions of
Nature dictate all motion laws defined onM. The process that symmetries determine the
geometries ofMand the associated vector bundles is achieved in the following three steps:
1) The symmetric principles, such as the Einstein general relativity, the Lorentz invari-
ance, and the gauge invariance, determine that the fields reflecting geometries ofM