Gravitation as a Many Body Problem

TL;DR

This paper proposes viewing gravitation as a many-body problem using operator matrices, drawing parallels with quantum integrable systems, and introduces a new mathematical framework for gravitational mechanics.

Contribution

It introduces a novel mathematical approach to gravity based on operator matrices and links it to quantum integrable systems like QISM.

Findings

Identification of a matrix operator framework for gravity

Connection between gravitational emission processes and Baxter equations

Similarity between gravitational mechanics and quantum integrable models

Abstract

The idea of viewing gravitation as a many body phenomenon is put forward here. Physical arguments supporting this idea are briefly reviewed. The basic mathematical object of the new gravitational mechanics is a matrix of operators. Striking similarity of the method of R-matrix (QISM) to the mathematical formulation of the new gravitational mechanics is pointed out. The s-wave difference Schrodinger equation describing a process of emission of radiation by a gravitating particle is shown to be analogous to the Baxter equation of the QISM.