# Canonical gravity and scalar fields

## TL;DR

This paper develops a new canonical variable framework for gravity and scalar fields within ADM formulation, enabling combined quantization of geometry and scalar fields, advancing the understanding of quantum gravity.

## Contribution

Introduces a novel canonical variable approach ({FFF}, {FFF}) for gravity and scalar fields, facilitating their unified quantization.

## Key findings

- Quantization of geometry and scalar fields achieved.
- New canonical variables simplify the combined theory.
- Framework supports implicit time dependence in quantum gravity.

## Abstract

A combined variable theory of gravity and scalar field is developed under ADM formulation by redefining new canonical conjugate variables ({\Phi}, {\Pi}). It is a dynamical theory of the space-matter with implicit time dependence. Quantizing this new field theory results in quantization of geometry and scalar field combined.