Physics NotePublished
Vertex Operator Representation of the Soliton Tau Functions in the Toda Models by Dressing Transformations
H. Belich Jr; G. Cuba; R. Paunov
1997
Publication details
- Authors
- H. Belich Jr; G. Cuba; R. Paunov
- Type
- Physics Note
- Status
- Published
- Publication date
- 1997
- Description
- Affine Toda theories based on simple Lie algebras <math>\mathcal{G}</math> are known to possess soliton solutions. Toda solitons has been found by Olive, Turok and Underwood within the group--theoretical approach to the integrable field equations. Single solitons are created by exponentials of special elements of the underlying affine Lie algebra which diagonalize the adjoint action of the principal Heisenberg subalgebra. When <math>\mathcal{G}</math> is simply laced and level one representations are considered, the generators of the affine Lie algebra are expressed in terms of the principal Heisenberg oscillators. This representation is known as vertex operator construction. It plays a crucial role in the string theory as wel as in the conformal field theory. Alternatively, solitons can be generated from the vacuum by dressing transformations. The problem to relate dressing symmetry to the vertex operator representation of the tau functions for the sine–Gordon model was previously considered by Babelon and Bernard. In the present paper, we extend this relation for arbitrary <math>A_n ^{(1)}\,\!</math> Toda field theory.
- Year
- 1997
- Number
- CBPF-NF-061/97
- Linked to a thesis
- No
- Linked to a grant
- No