Chapter 4
Unified Field Theory of Four
Fundamental Interactions
Once again, the goal of this book is to derive experimentallyverifiable laws of Nature based
on a few fundamental mathematical principles. The aims of this chapter are are as follows:
- to address the basic principles for the unified field theory coupling the four fundamental
interactions, - to derive the unified model based on these principles, and
- to study the mechanism and nature of individual interactions.
This chapter is based entirely on the recent work of the authors (Ma and Wang,2015a,
2014h,c,2013a,2014e). The key ingredients of the unified field theory include the following.
First, we have established two new principles, the principle of interaction dynamics (PID)
and the principle of representation invariance (PRI). PID was first discovered by (Ma and Wang,
2014e,2015a). It requires that for the four fundamental interactions, the variation be taken
under the energy-momentum conservation constraints. The validity of PID for the four fun-
damental interactions of Nature has been demonstrated through strong experimental and ob-
servation supports. For gravity, PID is induced by the presence of the dark matter and dark
energy phenomena. PID is also required by the Higgs field and the quark confinement, as we
explained in Chapter 1.
PRI, originally discovered by (Ma and Wang,2014h), states that theSU(N)gauge theory
should be invariant, under the representation transformations of the generator bases. PRI is
simply a logic requirement for theSU(N)theory.
Second, with PRI, the unification through a large symmetry group appears to be not fea-
sible. Then we have demonstrated that the two first principles, PID and PRI, together with
the principle of symmetry-breaking, offer an entirely different route for the unification:
1) the general relativity and the gauge symmetries dictate theLagrangian;
and