Spinors and Pre-Metric Electromagnetism

A Note on Metric Connections for Chiral and Dirac Spinors

By means of (1.2) and (1.3) each matrix S ∈ SL(2,C) is associated with some matrix S ∈ SO(1, 3,R) so that we can write S = φ(S), see [1], [2], and [3] for detailed description of this construction. Let M be a space-time manifold, i. e. a four-dimensional orientable manifold equipped with a pseudo-Euclidean Minkowski-type metric g and carrying a special smooth geometric structure which is called...

Harmonic spinors and local deformations of the metric

Let (M, g) be a compact Riemannian spin manifold. The AtiyahSinger index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

Unified Description of Gravitation and Electromagnetism through a Symmetric Metric

If gravitation and electromagnetism are both described in terms of a symmetric metric tensor, then the deflection of an electron beam by a charged sphere should be different from its deflection according to the Reissner-Nordstrøm solution of General Relativity. If such a unified description is true, the equivalence principle for the electric field implies that the photon has a nonzero effective...

SPINORS and

Metric Unification of Gravitation and Electromagnetism Solves the Cosmological Constant Problem

We first review the cosmological constant problem, and then mention a conjecture of Feynman according to which the general relativistic theory of gravity should be reformulated in such a way that energy does not couple to gravity. We point out that our recent unification of gravitation and electromagnetism through a symmetric metric tensor has just this property that energy in any form does not...