Torus invariance for the Clifford algebra, II


Journal Article

The structure of the representations of the infinite-dimensional Clifford algebra generated by states symmetric about a basis is studied. In particular, it is shown where they fit into the Gårding-Wightman classification. These representations have an unusual structure: the fibres are all infinite tensor product spaces, but the fibres corresponding to points on different orbits of the underlying group are different separable subspaces of the same inseparable infinite tensor product space. A procedure is given for constructing a large class of other representations of similar structure in which the torus automorphisms are unitarily implementable. In all cases the torus invariance depends on the geometric structure of the fibres, not on the underlying measure. © 1971.

Full Text

Duke Authors

Cited Authors

  • Reed, MC

Published Date

  • January 1, 1971

Published In

Volume / Issue

  • 8 / 3

Start / End Page

  • 450 - 468

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

International Standard Serial Number (ISSN)

  • 0022-1236

Digital Object Identifier (DOI)

  • 10.1016/0022-1236(71)90006-1

Citation Source

  • Scopus