Quantization of conformal general relativity is studied. The components of spin connectivity are considered to be the basic variables of quantum gravity. Their properties are analyzed and the dynamic part is highlighted. The work also uses tetrad formalism and the Arnovitt-Deser-Misner formalism. The gravitational action turns out to be quadratic in the components of the spin connection. Secondary quantization of the gravitational field is performed in terms of spin connectivity and further prospects for this approach are discussed.
04.90.+e Other topics in general relativity and gravitation
$^1$Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
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