Waves, particles and fields: an explicitly covariant approach

The idea of associating particle trajectories with wave propagation rays exploited in a previous paper in the context of general relativity with a synchronous gauge, here is examined with no assumptions on co-ordinate choice (no synchronous gauge condition on the metric). Identification of particle Hamilton–Jacobi equation with wave-sheet equation in a space–time with more than 4 dimensions, is performed in an explicitly covariant formulation, leading to a Kaluza–Klein type theory involving Klein–Gordon equation arising from dilaton field equations. De Broglie and Einstein-Planck quantum relations are also deduced in a natural way. Adding suitable Yang–Mills fields provides unification of gravitational, electromagnetic, weak and strong interactions into a $16$ dimensional space–time geometry. The electron mass gap is also avoided compactifying extra dimensional co-ordinates on fractalized closed paths.