A Concept of Explaining the Properties of Elementary Particles in Terms of Manifolds

Abstract

Abstract The authors propose to explain the magnetic moment of elementary particles by a suitable choice of one pseudo-riemannian manifold - the space of observations - and two general Riemannian manifolds - the spaces of the particle connected with the external electromagnetic and nuclear fields, respectively. By a general Riemannian manifold the authors understand a Riemannian manifold whose associated tensor field is allowed to be degenerate. In this way the mass of a particle as well as its electromagnetic and nuclear properties are determined by means of manifolds and mappings between the corresponding Hilbert spaces. A nuclear reaction is then to be interpreted as a mapping between the corresponding pseudo-riemannian manifolds and the associated general Riemannian manifolds. The proposal, competitive to the quantum field theory, presents a different way of describing the properties of physical objects. At the moment it is difficult to decide whether this proposal will lead to a satisfactory explanation of more physical phenomena than those explained by means of the quantum field theory, since it needs further research.