nLab
Dirac interaction picture

Idea

Dynamics in physics affects both observables and, dually, states; this is most well known in quantum physics but applies equally well to classical physics. The different “pictures” of physics differ in how the dynamics is explicitly formalized:

• In the Schrödinger picture, states are propagated through time?, while observables are held fixed; the axiomatic formalization of this is given by cobordism category representations in FQFT.

• In the Heisenberg picture, the dependence of observables on time (or more generally spacetime) is encoded, while the state is held fixed; the axiomatic formalization of this is given by the Haag–Kastler axioms of AQFT.

• The Dirac (interaction) picture is a mixture of these two approaches: dynamics is split into a free (or otherwise solvable) part and an interaction or perturbation; one of these is take to affect the states, the other the observables.

The pictures are named after those physicists who first used or popularised these approaches to quantum physics.

Formulation

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References

For instance section 7.19.3 in

• Eberhard Zeidler, Quantum field theory. A bridge between mathematicians and physicists – volume I Springer (2009) (web)