PauliSimplify
PauliSimplify[exp]
simplifies products of Pauli matrices and expands non-commutative products. Double indices and vectors are contracted. The order of the Pauli matrices is not changed.
See also
Overview, PauliSigma, PauliTrick.
Examples
CSIS[p1] . CSI[i] . CSIS[p2]
PauliSimplify[%]
(σ⋅p1).σi.(σ⋅p2)
(σ⋅p1).σi.(σ⋅p2)
CSIS[p] . CSI[i, j, k] . CSIS[p]
PauliSimplify[%]
(σ⋅p).σi.σj.σk.(σ⋅p)
−p2σi.σj.σk+2pkσi.σj.(σ⋅p)−2pjσi.σk.(σ⋅p)+2piσj.σk.(σ⋅p)
PauliSimplify[CSIS[p] . CSI[i, j, k] . CSIS[p], PauliReduce -> False]
−p2σi.σj.σk+2pkσi.σj.(σ⋅p)−2pjσi.σk.(σ⋅p)+2piσj.σk.(σ⋅p)
CSID[i, j, i]
PauliSimplify[%]
σi.σj.σi
3σj−Dσj
CSID[i, j, k, l, m, i]
PauliSimplify[%]
σi.σj.σk.σl.σm.σi
Dσj.σk.σl.σm−3σj.σk.σl.σm+2σj.σk.σm.σl−2σj.σl.σm.σk+2σk.σl.σm.σj