The Hausdorff formula for anticommutation is distinct from that for commutation. When dealing with anticommuting quantities A and B, the relationship simplifies to exp(A) = 1 + A, as higher-order powers vanish due to the property A^2 = 0 = B^2. The sign of the exponentials in the Hausdorff formula for anticommutation is indeed positive, confirming the user's initial assumption. This clarification is crucial for accurately applying the formula in quantum mechanics and related fields.
PREREQUISITESPhysicists, mathematicians, and students studying quantum mechanics or operator theory who seek to deepen their understanding of the distinctions between commutation and anticommutation in mathematical formulations.
If A and B are anti-commuting quantities, then I presume you also mean ##A^2=0 =B^2## ?mary1900 said: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?