Hausdorff formula for anticommutation

[mary1900]

hello. it's the first time I use this site I hope that I find the answer of my question: does the hausdorff formula for anti commutation have the same formula for commutation?

 

[mary1900]

I think the sign of the two exponentials must be positive,is it correct?
exp(A) B exp(A)= B + {A,B} + {A,{A,B}} +...

 

[strangerep]

hello. it's the first time I use this site I hope that I find the answer of my question: does the hausdorff formula for anti commutation have the same formula for commutation?

If A and B are anti-commuting quantities, then I presume you also mean $A^2=0 =B^2$ ?

If so, then $\exp(A) = 1 + A$ (since higher order powers vanish). That simplifies all formulas considerably...