Conserving Vector Current and Non-Linear Gauge Field
Ryôyû Utiyama · Progress of Theoretical Physics · 1971
Non-linear field equations of a set of vector fields Aaµ are derived from simple linear equations by a requirement of the mathematical consistency between the field equations and the conservation of the vector currents Jaµ which are the sources of the vector fields Aaµ. It is very interesting that the non-linear equations thus obtained are completely the same as those of the non-abelian gauge fields which are currently derived from the different postulate that the equations should be invariant under the extended gauge transformation. It is shown that the non-linear character of Aaµ gives rise to the quantization of the Qa-charge possessed by any field ϕA which interacts with Aaµ-field regardless of the nature of ϕA.