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 groupG 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\(\mathfrak{g}\) ofG so thatG and\(\mathfrak{g}\) 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\(\mathfrak{g}\) is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.
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Communicated by R.H. Dijkgraaf
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Alvarez, O., Liu, CH. Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism: I. Remnants of duality at the classical level. Commun.Math. Phys. 179, 185–213 (1996). https://doi.org/10.1007/BF02103719
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DOI: https://doi.org/10.1007/BF02103719