Abstract
The spectrally passive, gauge-invariant, quasi-free stases ω on the C*-algebra of anticommutation relations with respect to a one-parameter quasi-free action τ are described. If the one-particle Hamiltonian H is discrete, the precise condition on the one-particle density Q of ω is combinatorial, but if the Connes spectrum of τ is non-zero, it implies that Q = (I+e^{β (H+T)})^{–1} for some β ≥ 0 and some operator T of bounded trace norm, apart from some degenerate possibilities. If H has both discrete and continuous parts, these results can be combined with those of de Cannière for the purely continuous case.
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