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Bosonization on the lattice fermion - a rigorous mapping

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An inquiry: usually the bosonization is done on the field theory side. The mapping between the fermion operator to the boson operator is done for the field theory operators.

As far as we know for the bosonization on the lattice fermion, do we know whether there is any exact result about the rigorous mapping: from the lattice fermions to a lattice boson?

Any recommended approach or Ref on the rigorous "bosonization on the lattice fermion"?

ps. I have some fair understanding of uses of field theory Bosonization. Just wonder the lattice side procedure how well is it rigorous studied. Thank you!

This post imported from StackExchange Physics at 2014-06-06 07:13 (UCT), posted by SE-user Idear
asked Jun 6, 2014 in Theoretical Physics by wonderich (1,400 points) [ no revision ]
by Ref searching, I can find, for example, Lattice Bosonization, Bosonization on a lattice: The emergence of the higher harmonics, Bosonization and the lattice Gross-Neveu model, etc. But here I simply wish to have experts to comment about this Bosonization on the lattice fermion and in a rigorous view.

This post imported from StackExchange Physics at 2014-06-06 07:13 (UCT), posted by SE-user Idear

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