1. Interaction Picture – Review Assume that we know solution.

2. Equation of Motion Group properties Integrate

3. Operator Equation of Motion Solve by iteration: Messy Limits Area to be integrated over Integrate in the other direction to cover the same area

4. Time Ordered Product Change dummy variables Definition of time ordered product. Solution:

5. Adiabatic Turn on of Interaction At Letthen: Time independent stationary states Schrodinger picture

6. Gell-Mann/Low Theorem Question: Does the limit ε→0 have any meaning? Answer: Gell-Mann/Low Theorem If the following exists to all orders of perturbation theory: Then the following is an eigenstate of the full Hamiltonian: Needed to cancel infinite phase