Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The commutator formula states that for $A,B$ elements of a Lie algebra,

$$ \lim_{n\to \infty}\left\{ \exp\left(-A\tfrac{t}{n}\right)\exp\left(-B\tfrac{t}{n}\right)\exp\left(A\tfrac{t}{n}\right)\exp\left(B\tfrac{t}{n}\right)\right\}^{n^2}=\exp\left(t^2[A,B]\right)$$

I am interested in the case where $A=iH_1$ and $B=iH_2$ with $H_i$ self-adjoint. For finite dimensions the above certainly holds, but what happens in infinite dimensions? Under which conditions? Bounded/unbouded operators? I know that Trotter's formula has some complications in infinite dimensions, I'd be very thankful for any hints here.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.