Chapter 10

THE EQUATION OF MOTION FOR THE WG ORIGINAL PARTICLE  

    Since the WG original particle possesses mass mW= 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 WG original particle

 

  ;     (10-3)  

Using the definition of field intensity

      Fμν = μ Aν - ∂νAμ

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

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

       (□ μ2) A  = 0

       (□ μ2) ψ  = 0            (10-.5)

 For static WG, equation reduces to 

                   (10-.6) 

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

     image077.gif (1322 bytes)       (10-7)

  Gimage078.gif (934 bytes) = image079.gif (1291 bytes)   (10-8)

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

     image0710.gif (1314 bytes)               (10-9)

      Where g is a quantity, characterizing the strength of field intensity. The static field intensity is image0711.gif (1823 bytes)                                                                    `          `                                                              (10-10)

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