Field theory onR�S 3 topology: Lagrangian formulation

A brief description of the ordinary field theory, from the variational and Noether's theorem point of view, is outlined. A discussion is then given of the field equations of Klein-Gordon, Schrodinger, Dirac, Weyl, and Maxwell in their ordinary form on the Minkowskian space-time manifold as well as on the topological space-time manifold R × S3 as they were formulated by Carmeli and Malin, including the latter's most general solutions. We then formulate the general variational principle in the R × S3 topological space, from which we derive the field equations in this space.