Interaction picture as any other operator. In particular, let and be the density matrices in the interaction picture and the Schrödinger picture respectively. If there is probability to be in the physical state |"ψ"〉, then Transforming the Schrödinger equation into the interaction picture gives which states that in the interaction picture, a quantum state is evolved by the interaction part of the Hamiltonian as expressed in the interaction picture. If the operator "A" is time-independent (i.e., does not have "explicit time dependence"; see above), then the corresponding time evolution for "A"("t") is given by In the interaction picture the operators evolve in
Algebra of physical space equation, for an electrically charged particle of mass "m" and charge "e", takes the form: where e is an arbitrary unitary vector, and "A" is the electromagnetic paravector potential as above. The electromagnetic interaction has been included via minimal coupling in terms of the potential "A". The differential equation of the Lorentz rotor that is consistent with the Lorentz force is such that the proper velocity is calculated as the Lorentz transformation of the proper velocity at rest which can be integrated to find the space-time trajectory formula_31 with the additional use of Algebra of physical space In physics, the