The fundamental gravitino and its physical dark world
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.
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
We get the basic equation for the FG original particle
Using the definition of field intensity
F¦Ì¦Í = ∂¦Ì A¦Í - ∂¦ÍA¦Ì
Under the Lorentz gauge, the equation of motion for FG original particle can be expressed in terms of electromagnetic potential A¦Ì.
(¡õ ¨C ¦Ì2) A = 0
(¡õ ¨C ¦Ì2) ¦× = 0 (10-.5)
For static FG, equation reduces to
Therefore the Green function of FG equation, i.e. the responsive function of a point source G (r-r¡¯) satisfies the following equation
G = (10-8)
If the origin of the coordinate is put on the source point, the static potential can be rewritten
Where g is a quantity, characterizing the strength of field intensity. The static field intensity is:
Where (¦Ì r) is a dimensionless quantity, and ¦Ä<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¡±.