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 The fundamental gravitino and its physical dark world

Chapter 10

THE EQUATION OF MOTION FOR THE FG ORIGINAL PARTICLE  

    Since the FG original particle possesses mass mF= 3.6 x 10-45 kg, we can use the Lagrangian of generalized Maxwell electromagnetic field to describe this mass.

                         (10-1)

It is worth mentioning that the term   in (10-1) violates U (1) gauge invariant. There exists an essential difference between Lagrangian (10-1) and that in the Maxwellian theory. Making use of the Euler- Lagrange equation

                           (10-2)

We get the basic equation for the FG original particle

 

  ;      (10-3)  

Using the definition of field intensity

      F̦ A - ∂A

      A=(,A)                                           (10-.4)

    Under the Lorentz gauge, the equation of motion for FG original particle can be expressed in terms of electromagnetic potential A. 

       ( C 2) A  = 0

       ( C 2)   = 0                               (10-.5)

 For static FG, equation reduces to 

                                        (10-.6) 

      Therefore the Green function of FG equation, i.e. the responsive function of a point source G (r-r) satisfies the following equation

                 (10-7)

  G =         (10-8)

If the origin of the coordinate is put on the source point, the static potential can be rewritten

                           (10-9)

      Where g is a quantity, characterizing the strength of field intensity. The static field intensity is:

       (10-10)

Where ( r) is a dimensionless quantity, and <1. Assuming FG original particle cannot drag the FG ether too strongly, this means g=0. In the following I will mainly put forward the gravitational effect of FG.