Internal geometric current,and the Maxwell equation as a Hamiltonian system on configuration surfaces

Internal tension tensors on Riemannian manifolds with magnetic field are defined by means of a quantization mapping and quantum statistical averaging. The internal geometric density, current, and stress are derived from asymptotic expansions of the corresponding quantum tensors in the quantization parameter. On Riemannian surfaces with magnetic field, the Maxwell-Lorentz equation is interpreted as a Hamiltonian system. The effect of geometric superconductivity is discussed. The research was supported by the Russian Foundation for Basic Research under grant no. 05-01-00918.