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Mathematics of Quantization and Quantum Fields by Christian Gérard, Jan Derezinski

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15

Clifford relations

Clifford algebras and Clifford relations were studied by mathematicians long before canonical anti-commutation relations were considered by physicists. Actually, the “(neutral) CAR representations” that we introduced in Def. 12.1 could be called “representations of self-adjoint Clifford relations”.

We will use the name “Clifford relations” for anti-commutation relations identical to those of Def. 12.1, but without assuming that the underlying vector space is real, the corresponding operators are self-adjoint or that they even act on a Hilbert space.

In our short presentation we will restrict ourselves mostly to Clifford relations over finite-dimensional pseudo-Euclidean spaces. Our main motivation is to describe spinor ...

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