Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-05-21
Nucl.Phys. B415 (1994) 734-780
Physics
High Energy Physics
High Energy Physics - Theory
49 pages, CLNS 93/1220
Scientific paper
10.1016/0550-3213(94)90308-5
We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occuring at the free fermion point. We describe how radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebra split into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector. The space of fields in the anti-periodic sector can be organized using level-$1$ highest weight representations, if one supplements the $\slh$ algebra with the usual local integrals of motion. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. This leads to a new way of computing form-factors, as vacuum expectation values in momentum space.
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