Volume-Preserving Diffeomorphisms' versus Local Gauge Symmetry
Abstract
We present a new form of Quantum Electrodynamics where the photons are composites made out of zero-dimensional scalar ``primitives''. The r\ole of the local gauge symmetry is taken over by an infinite-dimensional global Noether symmetry -- the group of volume-preserving (symplectic) diffeomorphisms of the target space of the scalar primitives. Similar construction is carried out for higher antisymmetric tensor gauge theories. Solutions of Maxwell's equations are automatically solutions of the new system. However, the latter possesses additional non-Maxwell solutions which display some interesting new effects: (a) a magneto-hydrodynamical analogy, (b) absence of electromagnetic self-energy for electron plane wave solutions, and (c) gauge invariant photon mass generation, where the generated mass is arbitrary.
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