Talk:CCR and CAR algebras
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Clifford algebra=CCR algebra? Weyl algebra= CAR algebra?
[edit]CCR algebra = complex Weyl algebra over a complex vector space, equipped with dagger operation, so it becomes a *-algebra.
CAR algebra = complex Clifford algebra over a complex vector space, equipped with dagger operation, so it becomes a *-algebra.
Is this right? Or do we merely have that the Weyl algebra injects into the CCR algebra, and the addition of the adjoints considerably extends the size of the Weyl algebra to become the CCR algebra? The relationship is not stated very clearly in the article. 84.226.185.221 (talk) 15:51, 20 September 2015 (UTC)
- Wrong. The anticommutator (resp. commutator) in a CCR/CAR algebra matches with the Hermitian inner product. For a complex Weyl or Clifford algebra over a complex vector space, the inner product is symmetric. 84.226.185.221 (talk) 06:14, 21 September 2015 (UTC)