Thsi is a contributed topic in progress on representations of anti-commutation relations (CAR). (See also previous entries on the representations of canonical commutation and anti-commutation relations (CCR, CCAR)).

Representations of Canonical Anti-commutation Relations (CAR)

CAR Representations in a Non-Abelian Gauge Theory

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.

Bibliography

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