BOSONIZATION OF FERMI SYSTEMS IN ARBITRARY DIMENSION IN TERMS OF GAUGE FORMS

We present a general method to bosonize systems of fermions with infin itely many degrees of freedom, in particular systems of non-relativist ic electrons at positive density, by expressing the quantized conserve d electric charge- and current density in terms of a bosonic antisymme tric tenser field of rank d - 1, where d is the dimension of space. Th is enables us to make concepts and tools from gauge theory available f or the purpose of analysing electronic structure of non-relativistic m atter. We apply our bosonization identities and concepts from gauge th eory, such as the Wegner-'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London su perconductors, etc. Among our results are an exact formula for the pla smon gap in a metal, a simple derivation of the Anderson-Higgs mechani sm in superconductors, and an analysis of the orthogonality catastroph e for static sources.