One can also provide a representation of canonical anti-commutation relations in a non-Abelian
gauge theory defined on a non-simply connected region in the two-dimensional Euclidean space.
Such representations were shown to provide also a mathematical expression for the non-Abelian,
Aharonov-Bohm effect ([6]). Supersymmetry theories admit both CAR and CCR representations.
Note also the connections of such representations to locally compact quantum groupoid
representations.
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[11] Vainerman, L. 2003, Locally Compact Quantum Groups and Groupoids:
Contributed Lectures., 247 pages; Walter de Gruyter Gmbh and Co, Berlin.
(commutative and non-commutative quantum algebra, free download at this web link)