Interaction Picture Review

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
At
Time independent stationary states
Let
then
Schrodinger picture
6
Gell-Mann/Low Theorem
Question Does the limit e?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