Representations of canonical anti-commutation relations (CAR)RepresentationsOfCanonicalAntiCommutationRelationsCAR2009-04-07 11:51:052009-04-07 11:59:02TopicCARrepresentationsThsi is a contributed topic in progress on representations of anti-commutation relations (CAR). (See also previous entries on the representations of
\PMlinkname{canonical commutation and anti-commutation relations}{CanonicalCommutationAndAntiCommutationRepresentations} CCR).
\subsection{Representations of Canonical Anti-commutation Relations (CAR)}
\subsubsection{CAR Representations in a Non-Abelian Gauge Theory}
One can also provide a representation of canonical anti-commutation relations in a \PMlinkexternal{non-Abelian gauge theory}{http://planetphysics.org/?op=getobj&from=lec&id=124} 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
(\cite{GMS81}). Supersymmetry theories admit both CAR and CCR representations.
Note also the connections of such representations to
\PMlinkexternal{locally compact quantum groupoid representations.}{http://planetphysics.org/?op=getobj&from=lec&id=5}
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