Canonical path integral quantization of Einstein's gravitational field

TL;DR

This paper presents a novel path integral quantization method for Einstein's gravity that avoids gauge fixing and ambiguous determinants by using the Hamilton-Jacobi approach, simplifying the measure of integration.

Contribution

It introduces a new path integral quantization technique for Einstein's gravity that eliminates the need for gauge fixing and delta functions, providing a clearer measure of integration.

Findings

Path integral measure obtained without delta functions.

No gauge fixing required in the quantization process.

Avoids ambiguous determinants common in traditional methods.

Abstract

The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to obtain the measure of integration with no $\delta$- functions, no need to fix any gauge and so no ambiguous deteminants will appear.