Spectrum Generating Affine Lie Algebras in Massive Field Theory

Abstract

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 $\widehat{sl(2)}$ 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.

49 pages, CLNS 93/1220

References in corpus (3)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• The Quantum Double in Integrable Quantum Field Theory

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• An Algebraic Approach to Form Factors
• Particle-Field Duality and Form Factors from Vertex Operators
• Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example