Periods on manifolds, quantization, and gauge

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Abstract
It is suggested that the quantization of flux, charge, and angular momentum be interpreted as a set of independent natural concepts which physically exhibit certain topological properties of the fields on a space–time manifold. These quantum, or topological, properties may be described in terms of one‐, two‐, and three‐dimensional periods, respectively. In terms of this viewpoint, topological constraints between the one‐, two‐, and three‐dimensional periods can be put into correspondence with various gauge theories. If a dynamical system is to be nondissipative, in the sense that its one‐, two‐, and three‐dimensional topological periods are reversible invariants of the motion, then it is proved herein that the dynamical field V must be a Hamiltonian vector field, the field currents must be proportional to V, and the Lagrangian difference between the elastic and inertial energy density must be twice the interaction energy density, respectively.

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