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Bosonic Structure of a 2-Dimensional Fermion Model with Interaction among Different Speices
We study a massive Thirring-like model in 2-dimensional space-time, which
contains two different species of fermions. This model is a field theoretical
version of the quantum mechanical model originally proposed by Gl\"{o}ckle,
Nogami and Fukui, where different fermions interact with each other through
-function potentials. We derive a corresponding boson model by the
bosonization technique in the path integral formulation. This is a simple but
non-trivial extension of the freedom of the bosonization technique. Operator
correspondences between fermion and boson fields are given. One of these could
not be realistically expected from the naive correspondence of the original
single-species models. It is essential for this point that in our model
fermions of the same kind do not interact with each other directly. We find
that for a specific value of the coupling constant, one boson field becomes
free while the other is a Sine-Gordon field. For this case, therefore, our
two-species model is equivalent to the ordinary Sine-Gordon model of a single
boson field.Comment: Latex file, 11pages, no figure, needs ptptex.st
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