2.5. PRINCIPLE OF LAGRANGIAN DYNAMICS (PLD) 79
Remark 2.35.All current theories about interactions, concluding the Standard Model and
the String Theory, have a remarkable drawback: they cannot provide a set of acceptable
field equations for the weak and strong interactions from which we can deduce the weak and
strong interaction potentials. It is known that, the variational equations of the Yang-Mills
action (2.4.50)-(2.4.51) are in the form
(2.4.52)
∂μFμ νa −gλbcagα βFα νbGcβ−gJνa= 0 ,
(
iγμDμ−cm
̄h)
Ψ= 0 ,
where
Jνa=ΨγντaΨ, γν=gν βγβ.
However, it appears that we are not able to derive from (2.4.52) any weak and strong interac-
tion potentials in agreement with experiments. An important reason is that theSU(N)gauge
theory hasN^2 −1 fields:
(2.4.53) G^1 μ,···,Gkμ forK=N^2 − 1 ,
and we don’t know which or what combination of the potentialsin (2.4.53) gives rise to an
interaction force formula.
Remark 2.36.The authors have developed recently a new unified field theoryfor the four
fundamental interactions, based only on the following fundamental principles: the Einstein
Principle of General Relativity, the Principle of Lorentz Invariance, the Principle of Gauge
Invariance, and the two newly developed principles by the authors: the Principle of Interac-
tion Dynamics (PID) and the Principle of Representation Invariance (PRI). The unified field
theory will be presented in detail in Chapter 4 , and we shall see that the theory provides sound
explanations and resolutions to the following problems:
7.6.1 Dark energy and dark matter phenomena
2) spontaneous symmetry breaking based on first principles,3) quark confinement,4) asymptotically freedom,4.5.1 Strong interaction potential of elementary particles
6) layered formula for the weak and strong interaction potentials.2.5 Principle of Lagrangian Dynamics (PLD)
2.5.1 Introduction
PLD has been briefly introduced in Subsection2.1.3, and we now address PLD in detail.