interaction picture

This is because perturbative calculations are done in the interaction picture.

This definition conforms with the direct approach used in the interaction picture.

The next step is to find the Hamiltonian in the interaction picture, .

The interaction picture does not always exist, though.

The density matrix can be shown to transform to the interaction picture in the same way as any other operator.

It further serves to define a third, hybrid, picture, the Interaction picture.

A straightforward way to define the S-matrix begins with considering the interaction picture.

Let denote the evolution operator in the interaction picture.

This corresponds to the interaction picture in quantum mechanics.

Both Sehrödinger and interaction picture results are presented.

The interaction picture is useful in dealing with changes to the wave functions and observable due to interactions.

The name of the approximation stems from the form of the Hamiltonian in the interaction picture, as shown below.

From a mathematically rigorous perspective, there exists no interaction picture in a Lorentz-covariant quantum field theory.

Transforming the Schrödinger equation into the interaction picture gives:

In interacting quantum field theories, Haag's theorem states that the interaction picture does not exist.

Here a slightly more rigorous approach is taken in order to address potential problems that were disregarded in the interaction picture approach of above.

But since is to be regarded as a small perturbation, it is convenient to now use instead the interaction picture representation, in lowest nontrivial order.

In particular, let and be the density matrix in the interaction picture and the Schrödinger picture, respectively.

The previous remark only applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture.

Along with the decoupled-motions approximation, projected interaction picture density operators arc applied to inelastic scattering events.

The interaction Picture is most useful when the evolution of the observables can be solved exactly, confining any complications to the evolution of the states.

All three of these choices are valid; the first gives the Schrödinger picture, the second the Heisenberg picture, and the third the interaction picture.

The so-called Dirac picture or interaction picture has time-dependent states and observables, evolving with respect to different Hamiltonians.

It is evident that the expected values of all observables are the same in the Schrödinger, Heisenberg, and Interaction pictures:

The problem can be analyzed more easily by moving into the interaction picture, defined by the unitary transformation , where is an arbitrary operator, and .