Complete S-matrix of the massive thirring model

Breathers in the elliptic sine-Gordon model

“…In reverse, one should note that there exist many scalar theories which do not possess a known solitonic counterpart. One reason for that is, that the procedure [26,27] is not reversible and one can in general not construct the solitonic sector from the breather sector alone. Drawing a loose analogy to group theory one may think of the breather sector as a subgroup, which of course does not contain the information of a larger group in which it might be embedded.…”

“…We presume here that the particles related to the poles (4.9) are breathers and borrow some intuition from the classical theory, exploiting the fact that a breather is an oscillatory object made out of a superposition of a soliton and an antisoliton. For the sine-Gordon model this prescription was used in [27] to define the n th -breather particle creation operator. Even though we do not have a classical counterpart for the elliptic sine-Gordon model, we follow the same approach here and define the auxiliary state…”

“…Once the solitonic sector of a theory is constructed there is a well defined bootstrap procedure proposed by Karowski and Thun [26,27], which allows to complete the theory and to construct also the breather sector. There are numerous solutions known for a non-trivial soliton sector, since for instance for all affine Toda field theories with purely imaginary coupling constant the Yang-Baxter equations can be solved by representations of the corresponding quantum group [34,35,36].…”

“…In section 4 we discuss the soliton-antisoliton sector. Using a slightly modified procedure proposed originally by Karowski and Thun [26,27], the soliton-breather amplitudes are constructed in section 5 and the breather sector is discussed in section 6. By specifying the parameters to certain values we reduce the model in section 7 to several models.…”

The Form Factors and Quantum Equation of Motion in the Sine-Gordon Model

“…and two particle sine-Gordon S-matrix for the scattering of fundamental bosons (lowest breathers) [15] S(θ) = sinh θ + i sin πν sinh θ − i sin πν where θ is the rapidity difference defined by p 1 p 2 = m 2 cosh θ and ν is related to the coupling constant by ν = β 2 /(8π − β 2 ).…”