The history of the Baker-Campbell-Hausdorff (BCH) formula began in 1890 and involves Schur, Campbell, Poincaré, Baker, Pascal, Hausdorff, Yoshida and Dynkin. For real numbers we have z = log (exp (x) exp (y)) = x + y. However, matrices for Z = log (exp (X) exp (Y)) ≠ X + Y, except when they switch [X, Y] = XY-YX = 0. The formula BCH has infinite terms, although in many applications is truncated by a finite number of them.
You are viewing a single comment's thread from:
Yes,
And there are many ways to derive BCH formula.
In this post, using only some basic method, i.e., taylor expansion and integration by parts, I will derive BCH formula. [Of course there are much elegant way to prove this formula, as i cite in wiki and many standard Lie group textbooks]
Also, In the near future, I'd like to post about Dynkin diagram.