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

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

2008-04-11

arxiv.org/abs/0804.1962v3

Gen.Rel.Grav.41:1865-1886,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex2e, generalized from U(1)xSU(2) to U(1)xSU(d)

Scientific paper

10.1007/s10714-009-0757-2

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.

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