# Introduction to Gauge Theory of Gravitation

## TL;DR

This paper introduces gauge theory as a framework for understanding gravitation, extending Einstein's General Relativity to include spin interactions within a Riemann-Cartan spacetime.

## Contribution

It presents a gauge-theoretic approach to gravitation that incorporates spin and torsion, offering a unified perspective with the Standard Model.

## Key findings

- Gravitational interaction can be derived from gauge invariance principles.
- The theory predicts spin-gravity coupling in Riemann-Cartan spacetime.
- Extension of General Relativity to include torsion and spin interactions.

## Abstract

The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental interaction of gravitation is very well described by Einstein's General Relativity in a Riemannian spacetime metric, but General Relativity has been over time a gravitational field theory apart from the Standard Model. The theory of Gauge allows under symmetries of the group of Poincar\'e to impose invariances in the functional of the action of the spinor field that result in the gravitational interaction with the fermions. In this approach the gravitational field, besides being described by the equation similar to General Relativity, also brings a spin-gravitational interaction in a Riemann-Cartan spacetime.