A modification of Einstein-Schrodinger theory that contains Einstein-Maxwell-Yang-Mills theory

TL;DR

This paper extends the Lambda-renormalized Einstein-Schrodinger theory to non-Abelian gauge fields, closely approximating Einstein-Maxwell-Yang-Mills theory and potentially offering insights into dark matter.

Contribution

It generalizes the Einstein-Schrodinger theory to include non-Abelian fields with matrix-valued gauge potentials, maintaining gauge invariance and approximating Einstein-Maxwell-Yang-Mills theory.

Findings

The generalized theory closely approximates Einstein-Maxwell-Yang-Mills with negligible extra terms.

It can be coupled to Weinberg-Salam and GUT theories.

Small traceless parts of fields suggest a dark matter candidate.

Abstract

The Lambda-renormalized Einstein-Schrodinger theory is a modification of the original Einstein-Schrodinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein-Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of dxd Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein-Maxwell-Yang-Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein-Maxwell-Yang-Mills theory in that the extra terms in the field equations are 10^-13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg-Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.