Dyson operator

In quantum mechanics, suppose we have a Hamiltonian H which for some reason or other, we split into a "free" part H₀ and an "interacting" part H_int i.e. H=H₀+H_int. We will work in the interaction picture here.

Then, for t>t₀,

where is the time-ordering operator.

This is a perturbative series which typically diverges asymptotically. This is called the Dyson series.

Returning to the Schrödinger picture, for t_f > t_i,

This is the old-fashioned way of deriving the Feynman diagrams.