In quantum mechanics, the interaction picture (also known as the interaction representation or Dirac picture after Paul Dirac, who introduced it) is an intermediate representation between the Schrödinger picture and the Heisenberg picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the time dependence of observables. The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. Most field-theoretical calculations use the interaction representation because they construct the solution to the many-body Schrödinger equation as the solution to free particles in presence of some unknown interacting parts.

Equations that include operators acting at different times, which hold in the interaction picture, don't necessarily hold in the Schrödinger or the Heisenberg picture. This is because time-dependent unitary transformations relate operators in one picture to the analogous operators in the others.

The interaction picture is a special case of unitary transformation applied to the Hamiltonian and state vectors.

Haag's theorem says that the interaction picture doesn't exist in the case of interacting quantum fields.

Operators and state vectors in the interaction picture are related by a change of basis (unitary transformation) to those same operators and state vectors in the Schrödinger picture.

To switch into the interaction picture, we divide the Schrödinger picture Hamiltonian into two parts:

${\displaystyle H_{\text{S}}=H_{0,{\text{S}}}+H_{1,{\text{S}}}.}$

Any possible choice of parts will yield a valid interaction picture; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that H_0,S is well understood and exactly solvable, while H_1,S contains some harder-to-analyze perturbation to this system.