A groupoid approach to interacting fermions

Bram Mesland; Emil Prodan

doi:10.1007/s00220-022-04397-8

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arXiv · 2107.10681

A groupoid approach to interacting fermions

Bram Mesland·Emil Prodan

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Abstract

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by the inner-limit derivations over the ${\rm GICAR}$ algebra of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to the aperiodic lattice, we demonstrate that the image of $\dot \Sigma(\mathcal L)$ through the Fock representation can be completed to a groupoid-solvable pro-$C^\ast$-algebra. Our result is the first step towards unlocking the $K$-theoretic tools available for separable $C^\ast$-algebra for applications in the context of interacting fermions.

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BibTeX RIS

Bram Mesland, Emil Prodan. 2021-07-22. A groupoid approach to interacting fermions. https://doi.org/10.1007/s00220-022-04397-8

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