- #1

- 255

- 0

of Hausdorf-Campbell formula):

[tex]

\exp(X+Y) = \exp(-[X,Y]/2)\exp(X) \exp(Y)

[/tex]

It holds for any operator X, Y which commute with their commutator (i.e.

[tex] [X,[X,Y]]= [Y,[X,Y]] = 0[/tex]).

I look for a simple proof of this fact. Do you have any idea.

I also wonder if this formula is correct (for X,Y as before

such that [tex] [X,[X,Y]]= [Y,[X,Y]] = 0[/tex]):

[tex]

\exp(X) \exp(Y) = \exp([X,Y]) \exp(Y) \exp(X)

[/tex]

Thanks for help.