An Assessment of Evans’ Unified Field Theory I

Abstract

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ αβ . These two potentials yield the field strengths torsion T α and curvature R αβ . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic potentials A α ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.

The Einstein–yang–mills Equations From Bianchi Identities

“…Before proceeding further and generalizing the above the arbitrary SU (n) gauge groups, it is important to show the consistency of our above result with the recent criticism put forward by Hehl [22,23,24]. Hehl argued that the electromagnetic field strength cannot be simply related to the torsion of spacetime in a 4d spacetime.…”

An Assessment of Evans’ Unified Field Theory II

“…In an accompanying paper [4], called I in future, we investigated the unified field theory of Evans [1,2]. We take the notation and the conventions from I, where also more references to Evans' work can be found.…”

Elie Cartan's torsion in geometry and in field theory, an essay

“…Here in addition to the canonical energy-momentum current (33), the canonical spin current 3-form of matter…”

“…The right-hand sides describe the material sources of the Poincaré gauge gravity: the canonical energy-momentum (33) and the spin ( 40) three-forms. The left-hand sides are constructed from the gauge field momenta 2-forms…”