A Note on Gauge Principle and Spontaneous Symmetry Breaking in Classical Particle Mechanics

The U(1) gauge field is usually induced from the gauge principle, that is, the extension of global U(1) phase transformation for matter field. However the phase itself is realized only for quantum theory. In this paper we introduce the U(1) gauge field and gauge coupling from the gauge principle classically. The gauge symmetry is spontaneously broken from the out set. The Higgs mechanism occurs and we obtain the London equation. The Hydrodynamical interpretation of classical field we utilized is given, and the relation to super conductivity is discussed