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
Yukawa interaction explained by the fact that the Yukawa particle has spin zero and even spin always results in an attractive potential. The negative sign of the exponential gives the interaction an effectively finite range, so that particles at great distances will hardly interact any longer (interaction forces drop off exponentially with increasing separation). Now suppose that the potential formula_7 has a minimum not at formula_18 but at some non-zero value formula_19. This can happen, for example, with a potential form such as formula_20 with formula_9 set to an imaginary value. In this case, the Lagrangian exhibits spontaneous symmetry breaking. This is