The Fundamental Equations of Quantum Gravity

Vladimir Mikheev



1. Gravitational Radiation of Atom

The potentional energy of hydrogen-like atom equal to

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

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


2. Planck's interval 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

or we have

If we linearize the equation (1), we receive

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

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