The geometry of the Dirac equation is actually six-dimensional. Taking this hint it is shown that a six-dimensional-classical-field theory avoids the difficulties with which the Kaluza-Klein theory has to contend. Moreover, the possibility is gained of making the field energy of a point source finite. A geometric requirement (structure axiom) decomposes the six-dimensional continuum. The space-time world appears as a subspace, immersed in the six-dimensional space. Each world point corresponds to a sheet of physically indistinguishable points. Potentials and gauge transformation can be interpreted geometrically. As a consequence of the embedding, two fields of inertial forces (fields of constraint) occur. The one behaves just as the Maxwell field; the other has negative energy and can cancel the singularities of the electromagnetic one. The theory can be made conformally invariant and then yields a relation between the mass and the charges (the sources of the constraining fields). The presentation given in this paper is provisional, as it gives infinite range also to the field of negative energy.