FCSetPauliSigmaScheme[scheme]
allows you to specify how Pauli matrices will be handled in dimensions.
This is mainly related to the commutator of two Pauli matrices, which involves a Levi-Civita tensor. The latter is not a well-defined quantity in dimensions. Following schemes are supported:
"None"
- This is the default value. The anticommutator relation is not applied to dimensional Pauli matrices.
"Naive"
- Naively apply the commutator relation in -dimensions, i.e. . The Levi-Civita tensor lives in -dimensions, so that a contraction of two such tensors which have all indices in common yields .
Overview, PauliSigma, FCGetPauliSigmaScheme.
[] FCGetPauliSigmaScheme
[i, j, k]
CSID
[%, PauliReduce -> True] PauliSimplify
["Naive"]; FCSetPauliSigmaScheme
[] FCGetPauliSigmaScheme
= PauliSimplify[CSID[i, j, k], PauliReduce -> True] ex
// FCE // StandardForm
ex
(*I CLCD[i, j, k] + CSID[k] KDD[i, j] + 3 CSID[j] KDD[i, k] - D CSID[j] KDD[i, k] - 3 CSID[i] KDD[j, k] + D CSID[i] KDD[j, k]*)
["None"]; FCSetPauliSigmaScheme