Interaction Picture – Review Assume that we know solution.

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Presentation transcript:

Interaction Picture – Review Assume that we know solution.

Equation of Motion Group properties Integrate

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

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

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

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