# Unification of gravity and quantum field theory from extended noncommutative geometry

## TL;DR

This paper introduces an extended noncommutative geometric framework with biframes and quaternions to unify gravity and quantum field theory by distinguishing between ordinary and gravity spacetime frames.

## Contribution

It constructs a novel biframe spacetime with extended geometry, providing a geometric paradigm that unifies gravity and quantum fields within noncommutative geometry.

## Key findings

- The extended geometry distinguishes between ordinary and gravity spacetime frames.
- Fields in the biframe spacetime can be quantized and couple gravity with the standard model.
- Provides a new geometric approach to unify gravity and quantum field theory.

## Abstract

We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the standard model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such "flat" biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the standard model. Thus we provide a geometric paradigm in which gravity and the quantum field theory can be unified.