## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 33 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*