Mathematical Principles of Theoretical Physics

184 CHAPTER 4. UNIFIED FIELD THEORY

3) the action (4.1.11) also becomes the simple sum of these actions given in (4.1.5)-

(4.1.8):

(4.1.13) L(G 1 ,···,GN)→LEH+LEM+LW+LS.

For almost a century, a great deal of effort has been made to find the unified field model
based on the above mentioned approach. However, all effortsin this aspect are not successful.
In fact, among other reasons, this route of unification violates the principle of representation
invariance (PRI), discovered in (Ma and Wang,2014h); see also remaining part of this chapter
for details.
Moreover, the basic principles and the field equations from all attempted unified field the-
ories based on (4.1.9) are often too complex, and violate the simplicity principle of physics.
Most importantly, despite of many attempts, the current theories following (4.1.9) fail to
provide solutions to the following longstanding problems and challenges:

1) interaction force formulas

2) quark confinement,

3) asymptotical freedom,

4) strong interaction potentials of nucleus,

5) dark matter and dark energy phenomena,

6) decoupling to the individual interactions as required by(4.1.13),

7) spontaneous symmetry breaking from first principles,

8) mechanism of subatomic particle decay and scattering,

9) violation of PRI, and

10) reasons why leptons do not participate in strong interactions.

Unified Field Theory based on PID, PRI and PSB

The unified field theory introduced in this chapter is based onthe three new principles,
PID, PRI and PSB, postulated recently by the authors. In thistheory, the Lagrangian is a
simple sum of the known four actions in in (4.1.5)-(4.1.8):

(4.1.14) L=LEH+LEM+LW+LS,

and with which the unification is achieved as follows:

(4.1.15) Unification through the Field Equations Based on PID, PRI and PSB

A few remarks are now in order.