Authors: Malik Matwi
We derive the canonical momentum of the gravity field. Then we use it to derive the path integral of the gravity field. The canonical momentum is represented in Lorentz group. We derive it from the holonomy U(A) of the connection A of Lorentz group. We derive the path integral of gravity field as known in quantum fields theory and discuss the situation of free gravity field (like electromagnetic field). We find that this situation is only in the background spacetime, weak gravity, the situation of low matter density. We search for a theory in which the gravity field is a dynamical at any energy in arbitrary curved spacetime. For that, we suggest a duality gravity-area. That duality lets to possibility to study both gravity and area as dynamical fields in arbitrary curved spacetime. We find that the area field exists in the space-like and the gravity field exists in the time-like. We find that the tensor product of gravity and area fields, in selfdual representation, satisfies the reality condition. We derive the static potential of exchanging gravitons in scalar and spinor fields, the Newtonian gravitational potential.
Comments: 34 Pages. Damascus University, Syria
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