Torus invariance for the Clifford algebra, II

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.

Duke Scholars

Author Michael C. Reed Mathematics