Editing Interaction picture (section)

{{Short description|View of quantum mechanics}}
{{Quantum mechanics|cTopic=Formulations}}

In [[quantum mechanics]], the '''interaction picture''' (also known as the '''interaction representation''' or '''Dirac picture''' after [[Paul Dirac]], who introduced it)<ref name=":4">{{Cite book |last1=Duck |first1=Ian |url=https://archive.org/details/paulispinstatist0000unse/mode/2up |title=Pauli and the Spin-Statistics Theorem |last2=Sudarshan |first2=E.C.G. |publisher=World Scientific Publishing |year=1998 |isbn=978-9810231149 |pages=149–167 |language=en |chapter=Chapter 6: Dirac's Invention of Quantum Field Theory |author-link2=E.C.G. Sudarshan}}</ref><ref>{{cite web|url=https://courses.physics.illinois.edu/phys580/fa2013/interaction.pdf|title=Interaction Representation|website=courses.physics.illinois|archive-url=https://web.archive.org/web/20240524124921/https://courses.physics.illinois.edu/phys580/fa2013/interaction.pdf|archive-date=24 May 2024|url-status=live}}</ref> is an intermediate [[Dynamical pictures|representation]] between the [[Schrödinger picture]] and the [[Heisenberg picture]]. Whereas in the other two pictures either the [[Quantum state|state vector]] or the [[operator (physics)|operators]] carry time dependence, in the interaction picture both carry part of the time dependence of [[observable]]s.<ref>[[Albert Messiah]] (1966). ''Quantum Mechanics'', North Holland, John Wiley & Sons. {{ISBN|0486409244}}; J. J. Sakurai (1994). ''[[Modern Quantum Mechanics]]'' (Addison-Wesley) {{ISBN|9780201539295}}.</ref> The interaction picture is useful in dealing with changes to the [[wave function]]s and observables due to interactions. Most field-theoretical calculations<ref>J. W. Negele, H. Orland (1988), Quantum Many-particle Systems, {{ISBN|0738200522}}.</ref> use the interaction representation because they construct the solution to the many-body [[Schrödinger equation]] as the solution to the [[free-particle problem]] plus some unknown interaction 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 (quantum mechanics)|unitary transformation]] applied to the [[Hamiltonian mechanics|Hamiltonian]] and state vectors.

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