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Characteristic numbers ofU1-valued lattice gauge fields

Authors
Journal
Annals of Physics
0003-4916
Publisher
Elsevier
Publication Date
Volume
161
Issue
2
Identifiers
DOI: 10.1016/0003-4916(85)90086-7
Disciplines
  • Mathematics

Abstract

Abstract If a U 1-valued latice gauge field u defined on a periodic, 2-dimensional lattice satisfies the generic continuity condition uuuu ≠ − 1, it can be used to construct a principal U 1-bundle over the torus and in that bundle a connection such that parallel transport along bonds is given by u. In higher dimensions this construction can only be carried out if u is monopole-free (otherwise no such bundle can exist). The characteristic classes and numbers of this bundle can then be calculated from u in a straightforward way. Examples are given of u's with maximum possible characteristic numbers, along with a discussion of the behavior of u and of its topology under an action-decreasing deformation.

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