Séminaire Lotharingien de Combinatoire, B26f (1991), 5 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1992, 476/S-26, p. 63-67.]

T. Lulek and W. Florek

Gauge Symmetries in the Heisenberg Model of a Magnet

Abstract. A relation between geometric and gauge symmetries for the Heisenberg model of magnet is pointed out. The space of quantum states of the magnet exhibits the structure of a bundle, with the base consisting of nodes of the crystal, and the typical fiber spanned on the set of the single-node spin projections. The geometric symmetry group acts on the base, the gauge group - on the typical fiber, and all combined operations form the wreath product. In particular, all global gauge transformations yield the direct product group - a subgroup of the wreath product.

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