## Quantum Gravity Field

**Authors:** Malik Matwi

We study the dynamics of the gravity field according to the quantum fields theory on arbitrary spacetime $x^{\mu}$. Therefore, we suggest a canonical momentum $\pi _I$ as a momentum conjugate to the canonical gravity field $\tilde e^I = ee_{\mu}^I n^{\mu}$. We derive both the canonical gravity field and its conjugate momentum from the holonomy $ U\left( {\gamma ,A} \right)$ of the complex selfdual connection $ A_{a}^i$.
The canonical momentum $\pi _I$ is represented in the Lorentz group. We use it in deriving the path integral of the gravity field according to the quantum fields theory. Then, we discuss the situation of the free gravity field (like the electromagnetic field). We find that this situation takes place only in the background spacetime approximation, the situation of low matter density(weak gravity).
Then, we derive the Lagrange of the Plebanski two form complex field $\Sigma ^{i}$, which is represented in selfdual representation $\left| {\Sigma ^i } \right\rangle$. We try to combine the two fields(gravity and Plebanski) in one field: $K_{\mu}^i$.
Finally, we derive the static potential of exchanging gravitons in scalar and spinor fields, the Newtonian gravitational potential.

**Comments:** 31 Pages.

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### Submission history

[v1] 2018-05-30 19:26:39

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