I found this expression for the time-evolution operator:
$$\begin{split} U(t) & = T_{\leftarrow}\exp\left[-i\int_0^t ds H(s)\right] \\ &= \exp\left[-\frac{1}{2}\int_0^t ds\int_0^t ds' [H(s),H(s')]\theta(s-s')\right]\exp\left[-i\int_0^t ds H(s)\right]\end{split}$$
with $H$ Hamiltonian and $\theta(s-s')$ the Heaviside step function. The commutator of the Hamiltonian at two different times is a c-number function, I don't know if it's important.
Does anyone know how to get the last part?
