# Locally equivalent quasifree states and index theory

@article{Bourne2022LocallyEQ, title={Locally equivalent quasifree states and index theory}, author={Chris Bourne}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in KO*(Ar) with A a C*,r -algebra of allowed deformations. When A = C*(X), the Roe algebra of a coarse space X, and we…

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