#interaction picture

PHY2403H Quantum Field Theory. Lecture 14: Time evolution, Hamiltonian perturbation, ground state. Taught by Prof. Erich Poppitz

PHY2403H Quantum Field Theory. Lecture 13: Forced Klein-Gordon equation, coherent states, number density, time ordered product, pole shifting, perturbation theory, Heisenberg picture, interaction picture, Dyson's formula. Taught by Prof. Erich Poppitz

The plan of our paper is as follows.  A brief sketch of the history of Haag's theorem is given in Section 2. Haag's original proof is reviewed in Section 3, along with the Hall-Wightman version of the theorem. Section 4 is devoted to some clarifications of and qualifications to the theorem. Explanations for why the interaction picture and perturbation theory work, in spite of Haag's theorem, are explored in Section 5. Section 6 discusses differences in the formulations of scattering theory in QFT and ordinary QM that result from Haag's theorem. Section 7 examines the claim that Haag's theorem shows that non-Fock representations are required to describe interacting fields. Haag's theorem tells us that the choice among the unitarily inequivalent representations of the CCR depends on the dynamics. The question of whether the choice is fully determined by the dynamics is taken up in Section 8. Concluding remarks are given in Section 9. Some technical details of important concepts are provided in the Appendix.