Interaction picture - time evolution operator

Main Question or Discussion Point

Hey all,

I got some question referring to the interaction picture. For example:

I have the Hamiltonian $H=sum_k w_k b_k^\dagger b_k + V(t)=H1+V(t)$

When I would now have a time evolution operator:

$T exp(-i * int(H+V))$.

(where T is the time ordering operator)

How can I transform it into the interaction picture?

Do I have to calculate:

$exp[i H(1)t]T exp(-i int(H+V))exp[-i H(1)t]$

This is nearly impossible, isn't it?

Best

(is it possible to use latex here?)

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