Vertex Operators and Soliton Time Delays in Affine Toda Field Theory
نویسندگان
چکیده
In a space-time of two dimensions the overall effect of the collision of two solitons is a time delay (or advance) of their final trajectories relative to their initial trajectories. For the solitons of affine Toda field theories, the space-time displacement of the trajectories is proportional to the logarithm of a number X depending only on the species of the colliding solitons and their rapidity difference. X is the factor arising in the normal ordering of the product of the two vertex operators associated with the solitons. X is shown to take real values between 0 and 1. This means that, whenever the solitons are distinguishable, so that transmission rather than reflection is the only possible interpretation of the classical scattering process, the time delay is negative and so an indication of attractive forces between the solitons.
منابع مشابه
Toda Solitons: a Relation between Dressing transformations and Vertex Operators
Affine Toda equations based on simple Lie algebras arise by imposing zero curvature condition on a Lax connection which belongs to the corresponding loop Lie algebra in the principal gradation. In the particular case of A (1) n Toda models, we exploit the symmetry of the underlying linear problem to calculate the dressing group element which generates arbitrary N -soliton solution from the vacu...
متن کاملOn the Topological Charges of Affine Toda Solitons
We provide a proof of a formula conjectured in [1] for some coefficients relevant in the principal vertex operator construction of a simply-laced affine algebra ĝ. These coefficients are important for the study of the topological charges of the solitons of affine Toda theories, and the construction of representations of non-simply-laced ĝ and their associated Toda solitons.
متن کاملExact quantum S-matrices for solitons in simply-laced affine Toda field theories
We obtain exact solutions to the quantum S-matrices for solitons in simply-laced affine Toda field theories, except for certain factors of simple type which remain undetermined in some cases. These are found by postulating solutions which are consistent with the semi-classical limit, h̄ → 0, and the known time delays for a classical two soliton interaction. This is done by a ‘q-deformation’ proc...
متن کاملar X iv : m at h / 02 08 04 3 v 1 [ m at h . Q A ] 6 A ug 2 00 2 QUANTUM AFFINE
Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection algebras of type d (1) n to determine new n-parameter families of non-diagonal reflection matrices. These matrices describe the reflection of vector solitons off t...
متن کاملSoliton-preserving boundary condition in affine Toda field theories
We give a new integrable boundary condition in affine Toda theory which is soliton-preserving in the sense that a soliton hitting the boundary is reflected as a soliton. All previously known integrable boundary conditions forced a soliton to be converted into an antisoliton upon reflection. We prove integrability of our boundary condition using a generalization of Sklyanin’s formalism.
متن کامل