Form factors of local operators

M. Szőts, G. Takács

Atsushi Nakayashiki, Yoshihiro Takeyama

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.

Brian P. Anderson, David H. Sharp, Arthur S. Wightman

A.A. Cheshkov

Lorenzo Piroli, Pasquale Calabrese

We present exact formulas for the form factors of local operators in the repulsive Lieb–Liniger model at finite size. These are essential ingredients for both numerical and analytical calculations. From the theory of algebraic Bethe ansatz, it is known that the form factors of local operators satisfy a particular type of recursive relations. We show that in some cases these relations can be used directly to derive practical expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size. Our main results are determinant formulas for the form factors of the operators and Ψ R (0), for arbitrary integer R , where Ψ, are the usual field operators. From these expressions, we also derive the infinite size limit of the form factors of these local operators in the attractive regime.

Brian L. Silver