On the Quantum Theory of Gravitating Particles

TL;DR

This paper introduces a novel approach to gravitational mechanics by formulating a new eigenvalue problem that incorporates a fundamental length scale, leading to difference wave equations in a quantum gravity context.

Contribution

It proposes a new basis for gravitational mechanics with a unique eigenvalue problem involving a fundamental length, and introduces difference wave equations in the theory.

Findings

Eigenvalue problem includes fundamental length ${ m l}$

Derivation of new wave equations as difference equations

Provides a basis for quantum gravitational spectrum

Abstract

The present paper proposes a basis for new gravitational mechanics. The problem of finding the spectrum of mass-energy is reduced to a new kind of eigenvalue problem which intrinsically contains the fundamental length ${\it l} = \sqrt{Gh\over c^3}$.The new wave equations are difference wave equations in one representation of the theory.