## § Lie bracket commutator from exponentiation (WIP)

I thought this was quite cute. To make sense of $[a, b]$ we consider the expression $e^{\epsilon a} e^{\epsilon b} e^{- \epsilon a} e^{- \epsilon b}$ which is equivalent to:
\begin{aligned} &(1 + \epsilon a + \epsilon^2 a^2/2)(1 + \epsilon b+ \epsilon^2 b^2/2)(1 - \epsilon a + \epsilon^2 a^2/2)(1 - \epsilon b + \epsilon^2 b^2/2) \\ &[(1 + \epsilon a + \epsilon^2 a^2/2)(1 - \epsilon a + \epsilon^2 a^2/2)] [(1 + \epsilon b+ \epsilon^2 b^2/2)(1 - \epsilon b + \epsilon^2 b^2/2)] \\ &[((1 +\epsilon^2 a^2/2) + \epsilon a)((1 + \epsilon^2 a^2/2) - \epsilon a)] [(1 + \epsilon^2 b^2/2+ ) \epsilon b) ((1 + \epsilon^2 b^2/2) - \epsilon b)] \\ &[((1 +\epsilon^2 a^2/2)^2 - \epsilon^2 a^2)] [(1 + \epsilon^2 b^2/2^2 - \epsilon^2 b^2)] \\ \end{aligned}
TODO