Abstract
It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.
Original language | English (US) |
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Pages (from-to) | 185-213 |
Number of pages | 29 |
Journal | Communications in Mathematical Physics |
Volume | 179 |
Issue number | 1 |
State | Published - Jan 1 1996 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics