## 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 |

DOIs | |

State | Published - 1996 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics