Quantization of nonlinear tensor field equations - Geometric structure-integral with action-based selection

In Kaluza–Klein theory, the Lorentz force, Maxwell equations, and the electromagnetic energy-momentum tensor arise directly from the five-dimensional metric. This enables a virtually speculation-free approach to the quantization of nonlinear tensor field equations of Kaluza theory and general relativity using a generalization of Feynmans Integral with Einstein–Hilbert action. In nonlinear cases, wave–particle duality extends to a duality of spacetime and non-metric phase manifold structure, yielding a picture closely related to quantum field theory.Unlike the Feynman path integral, which maps the action integral to the phase of a wave function and remains gauge- and coordinate-dependent, the action integral itself is scalar and covariant. Direct quantization of this scalar action defines a structure integral with action-based selection and avoids the problems of interference and gauge.