General Relativity for N Properties

TL;DR

This paper develops a general analytical framework for characterizing properties using Grassmann variables in the context of general relativity, applicable for any number of properties N.

Contribution

It introduces an analytical method to determine coefficients in a gauge and gravitational field scheme for arbitrary N, avoiding complex algebraic computations.

Findings

Analytical expressions for coefficients for general N

Method simplifies calculations compared to algebraic software

Framework applicable to various properties in gravitational theories

Abstract

We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by $N$ anticommuting scalar Grassmann variables. We do this for general $N$, using analytical methods; this obviates the need for our algebraic computing package which can become quite unwieldy as $N$ is increased.