Uniqueness of the bosonization of the $U_q(su(2)_k)$ quantum current algebra

Details Uniqueness of the bosonization of the $U_q(su(2)_k)$ quantum current algebra Uniqueness of the bosonization of the $U_q(su(2)_k)$ quantum current algebra

1993-01-21

arxiv.org/abs/hep-th/9301087v1

Nucl.Phys. B404 (1993) 457-482

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1016/0550-3213(93)90487-A

Four apparently different bosonizations of the $U_q(su(2)_k)$ quantum current algebra for arbitrary level $k$ have recently been proposed in the literature. However, the relations among them have so far remained unclear except in one case. Assuming a special standard form for the $U_q(su(2)_k)$ quantum currents, we derive a set of general consistency equations that must be satisfied. As particular solutions of this set of equations, we recover two of the four bosonizations and we derive a new and simpler one. Moreover, we show that the latter three, and the remaining two bosonizations which cannot be derived directly from this set of equations since by construction they do not have the standard form, are all related to each other through some redefinitions of their Heisenberg boson oscillators.

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