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Interaction picture
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<p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, the interaction picture (also known as the interaction representation or Dirac picture after <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a>, who introduced it) is an intermediate <a href="/facts/Dynamical_pictures/xfb1c8Et">representation</a> between the <a href="/facts/Schr%25C3%25B6dinger_picture/4VK89MbE">Schrödinger picture</a> and the <a href="/facts/Heisenberg_picture/Y5XwceMA">Heisenberg picture</a>. Whereas in the other two pictures either the <a href="/facts/Quantum_state/7jbxd7Dx">state vector</a> or the <a href="/facts/Operator_(physics)/rCJw8UFz">operators</a> carry time dependence, in the interaction picture both carry part of the time dependence of <a href="/facts/Observable/fcBAsBjm">observables</a>. The interaction picture is useful in dealing with changes to the <a href="/facts/Wave_function/KgM5ykjY">wave functions</a> and observables due to interactions. Most field-theoretical calculations use the interaction representation because they construct the solution to the many-body <a href="/facts/Schr%25C3%25B6dinger_equation/3csgSIWF">Schrödinger equation</a> as the solution to the free-particle problem plus some unknown interaction parts. </p><p>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. </p><p>The interaction picture is a special case of <a href="/facts/Unitary_transformation_(quantum_mechanics)/DCzYRCxK">unitary transformation</a> applied to the <a href="/facts/Hamiltonian_mechanics/2ReerlNA">Hamiltonian</a> and state vectors. </p><p><a href="/facts/Haag%2527s_theorem/WwBr2oGe">Haag's theorem</a> says that the interaction picture doesn't exist in the case of interacting <a href="/facts/Quantum_field/VoewsNJV">quantum fields</a>. </p>