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. . . , θ6 and constructing two triples of σk = 2
i~ε klmθlθm, one for k, l,m ∈ {1, 2, 3} and one for k, l,m ∈ {4, 5, 6}. The four functions
defined as αk = σkσ4 for k = 1, 2, 3 and β = σ6, (2.161)
43 [...] inner and the outer product always have to be calculated first, i.e.
A ∧BC = (A ∧B)C 6= A ∧ (BC) and A ·BC = (A ·B)C 6= A · (BC). (4.12)
The formalism of geometric algebra briefly sketched so far can now [...] ∗C B1 = γ3γ2, B5 = I(4) ∗C B2 = γ1γ3, B6 = I(4) ∗C B3 = γ2γ1, (5.123)
with the pseudoscalar I(4) = γ0γ1γ2γ3, For these bivectors one has B2∗C 1,2,3 = 1, B2∗C
4,5,6 = −1 and
Bi × Bj = −εijk(I(4) ∗C Bk), …