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Myopic Bosonization

As the title suggests, this is an attempt at bosonizing fermions in any number of dimensions without paying attention to the fact that the Fermi surface is an extended object. One is tempted to introduce the density fluctuation and its conjugate and recast the interacting problem in terms of these canonical Bose fields. However, we find that the attempt is short-sighted figuratively as well for the same reason. But surprisingly, this flaw, which manifests itself as an inconsistency between Menikoff-Sharp's construction of the kinetic energy operator in terms of currents and densities, and our ansatz for this operator, is nevertheless able to reproduce(although reluctantly) many salient features of the free theory. Buoyed by this success, we solve the interacting problem and compute the full propagator.