Research proof index

Full Euclidean Levi-Civita contraction ∑_b (ε4)_b · (ε4)_b = 24 at the symbol level: summing the square of every standard-basis component of ε4 over all four Fin 4 index slots, paired naively (no metric), counts the 4! = 24 permutations. The Lorentz contraction ε^{μνρσ} ε_{μνρσ} lowers one factor with η and equals -24 instead.

Multiplying an element of SL(2, ℂ) on the left with the metric 𝓔 is equivalent to multiplying the inverse-transpose of that element on the right with the metric.

Contraction on the right with dualLeftLeftUnit does nothing.

Contraction on the right with dualRightRightUnit does nothing.

Contraction on the right with leftDualLeftUnit does nothing.

Contraction on the right with rightDualRightUnit does nothing.