The Fundamental Equations of Quantum Gravity

Vladimir Mikheev

mailto: mikh1952@gmail.com

 

1. Gravitational Radiation of Atom

The potentional energy of hydrogen-like atom equal to
(1)

where r  is a distance from electron to nucleus, Ze  is a nuclear charge, e is an electron charge, G  is a gravitational constant, m  is an electron mass, M  is a nuclear mass.

If we introduce


equality (1) will have the form

To solve a Schrodinger equation for radial wave functions


we receive energy levels
n = 1, 2, 3, ...

To take into consideration that

we have finally
(2)

The two last members of equality (2) define the gravitational radiation of atom.

 

2. Dirac Equation in Quantum Theory of Gravity

The rest mass of electron maybe equal


where h  is Planck's constant, c  is velocity of light, G  is gravitational constant, k  is numerical coefficient,

then Planck's four-dimensional interval


defines its limit of the localization in space-time.

If we utilize equality


Hamiltonian for free electron will have form
(1)

or we have

If we linearize the equation (1), we receive
(2)

where are Dirac matrices,    j = 1, 2, 3

For electron with charge e, which is in electromagnetic field, we do the substitution in equality (2)
   j = 1, 2, 3

Publication:
1. General Relativity and Gravitation, proceedings of the 12th International Conference on General Relativity and Gravitation, held July 2-8, 1989, in Boulder, Colorado, USA,
under the auspices of the International Society on General Relativity and Gravitation, 1989, p.703
2. Foundations of Gravitation and Cosmology. Abstracts of the reports at the International school-seminar. Odessa,September4-10 1995 Moscow, Russian Gravitational Society, 1995, p.112,113

Copyright  Vladimir Mikheev