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        "quote": "This is the tensor product of complex-valued functions on $\\mathbb R^d$, acted on by $\\operatorname{Weyl}(2d,\\mathbb C)$, and anticommuting functions on $\\mathbb C^d$, acted on by $\\operatorname{Cliff}(2d,\\mathbb C)$. The mutually adjoint operators $Q_+,Q_-$ square to zero. Mathematicians recognize this space as the complex differential forms $\\Omega^*(\\mathbb R^d)$, where the degree ranges from $0$ (functions) to $d$. The [<u class=\"concept-term\" data-concept-reference=\"concepts/differential-geometry/de-rham-differential\" data-concept-identity=\"urn:uuid:c4df2f3d-e41b-4bde-949e-8989739a863d\" data-concept-route=\"/concept-identities#concept-c4df2f3d-e41b-4bde-949e-8989739a863d\" id=\"first-f2d1370f98e339cb27f5-en\">de Rham differential</u>](../../../../../concepts/differential-geometry/de-rham-differential) $d$ squares to zero. The Euclidean inner product induces a Hermitian inner product on forms by integration; the adjoint $\\delta$ of $d$ also squares to zero. The [<u class=\"concept-term\" data-concept-reference=\"concepts/differential-geometry/hodge-laplacian\" data-concept-identity=\"urn:uuid:8a3364eb-be9a-4280-9185-16e79b63e191\" data-concept-route=\"/concept-identities#concept-8a3364eb-be9a-4280-9185-16e79b63e191\" id=\"first-07e3492ab6eae1bf3ee5-en\">Laplacian operator on differential forms</u>](../../../../../concepts/differential-geometry/hodge-laplacian) is",
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