#####
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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