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Classical non-linear sigma models on Grassmann manifolds of compact or non-compact type

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Antoine, Jean-Pierre [UCL] Piette, Bernard [UCL]

Grassmannian σ models are reexamined in the light of a new geometrical result. Namely, the Cartan immersion of a Riemannian symmetric space G/H into its isometry group G is not always a diffeomorphism onto the set Mσ introduced by Eichenherr and Forger [Nucl. Phys. B 164, 528 (1980)]. This is the case, in particular, for Grassmann manifolds of all types: their set Mσ is shown to be disconnected and its structure is completely analyzed. As a consequence, a new constraint must be introduced in the Bäcklund transformation (BT) method proposed by Harnad, Saint‐Aubin, and Shnider [Commun. Math. Phys. 92, 329 (1984)]. It is shown, however, to always be satisfied for Grassmann manifolds of compact type (i.e., G compact), but the problem remains open in most other cases. On the other hand, the BT method is extended to the Euclidean regime.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 1987
Journal information "Journal of Mathematical Physics" - Vol. 28, no. 11, p. 2753-2762 (1987)
Peer reviewed yes
Publisher American Institute of Physics ((United States) Melville)
issn 0022-2488
e-issn 1089-7658
Affiliation UCL - SC/PHYS - Département de physique
Links
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Bibliographic reference Antoine, Jean-Pierre ; Piette, Bernard. Classical non-linear sigma models on Grassmann manifolds of compact or non-compact type. In: Journal of Mathematical Physics, Vol. 28, no. 11, p. 2753-2762 (1987)
Permanent URL http://hdl.handle.net/2078/31415