Bi-quaternion form of electromagnetism theory

Abstract

Appling bi-quaternion,we have generalized the classical electromagnetism theory in the presence of electric charge only to a new electromagnetic-symmetry theory in the presence of both electric and magnetic charges.In the bi-quaternion formulation,the Hamiltonian action and corresponding Lagrangians of a system with both electric and magnetic charges are presented.Then form the action principle the field equations and the equations of motion of particle with electric-magnetic charge in electromagnetic field are derived.By analysis of these equations,it is shown that the new theory is consistent with the usual electromagnetism theory in the case of existing electric charge only,and that the new theory is not only the generalized classical theory,but it is also different from other electromagne-tism theories considering both electric and magnetic charges in principle.The important conclusions form the bi-quaternion theory are obtained,that the field produced by electric(or magnetic) charge does not act on the magnetic(or electric) charge,especially,there is no mutual action between the particle with electric charge and the particle with magnetic charge(monopole).Finally,we discuss three physics problems based on the new bi-quaternion electromagnetism theory:(i) A new explanation of the negative results of the experiments to search monopole is presented,in which the negative results cannot conclude no monopole exists,but may indicate the theory of the experiments need revise.(ii) A hypothesis that the monopole-like matter may be a kind of dark matter is given.(iii) The phenomena of fractional electric charges explain as existing particles with different kinds of electric-magnetic charges.