Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

Introduction Ampere,Faradayandotherphysicistsproposeda numberofexperimentallawsaboutelectromagnetism.OnthesebasesMaxwellestablishedMaxwell sequa tionsin1862.Meanwhile,accordingtomathematical theoreticalpointofview(consistencyofequations),hesupplementedelectromagnetismwithelectricdis placementvectors.Einsteinpointedoutthat,justaswhatthe ancientshadsaid,peoplemightgraspactualitybypure mathematicalthought.Butintheestablishmentof Maxwell sequations,mathematiciansplayedonlypar tiallyimportantrole…

Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codifferential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, respectively. The definitions of the divergence and the curl of a 2D surface flux of a tensor are obtained. Maxwell's equations, namely, the construction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law (mass or fluid flux quantity and so on) and the feature of central field (or its composition). By the feature of central field (or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory (a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces) are presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.