Some notes on many body theory
On Feynman diagram
- Why should we demand wick’s theorem? Isn’t the adiabatic evolution theorem in junior quantum mechanics course enough?
- The whole derivation of Feynman diagram should be placed on a solid ground, in order that the whole diagram analysis technic is exact.
- Wick’s theorem is a must, since we have no tools for handling ground state of a general interaction Hamiltonian. All derivation is based on our clear understanding of the non-interacting Hamiltonian — we wrote our creation & annihilation operators on that basis, we have to use them thereafter.
- How to give a rigorous definition of “topologically distinct Feynman diagram? ”
- I believe it’s not even necessary to give a definition. The “topologically equivalent” thing is nothing but another way of saying “if you do the integral, these two diagrams will contribute the same”. We just have to be patient, not to be given two diagrams which contribute the same, but insists on calling them “distinct” based on some definition.