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Birkhäuser Boston eBooks

On Form Factors of the SU(2) Invariant Thirring Model

Atsushi Nakayashiki, Yoshihiro Takeyama

Published Jan 1, 2002• 14 citations
Publisher

Abstract

Integral formulae for form factors of a large family of charged local operators in the SU ( 2 ) invariant Thirring model are given, extending Smirnov’s construction of form factors of chargeless local operators in the sine-Gordon model. New abelian symmetry acting on this family of local operators is found. It creates Lukyanov’s operators which are not in the above family of local operators in general.

DOI
10.1007/978-1-4612-0087-1_13

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Integral formulae for form factors of a large family of charged local operators in the SU ( 2 ) invariant Thirring model are given, extending Smirnov’s construction of form factors of chargeless local operators in the sine-Gordon model. New abelian symmetry acting on this family of local operators is found. It creates Lukyanov’s operators which are not in the above family of local operators in general.
Form Factors of SU(N)\textit{SU}(N)SU(N) Invariant Thirring Model
We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems.For that purpose, we consider the sine-Gordon model on a finite lattice and in finite dimensional cyclic representations as our main example.We first build our two central tools for computing matrix elements of local operators, namely, a generic determinant formula for the scalar products of states in the SOV framework and the reconstruction of local fields in terms of the separate variables.The general form factors are then obtained as sums of determinants of finite dimensional matrices, their matrix elements being given as weighted sums running over the separate variables and involving the Baxter Q-operator eigenvalues.