The discussion revolves around the topic of renormalization of bound states in quantum field theory (QFT), with a focus on approaches to understanding loop corrections and their implications for bound states, particularly in quantum electrodynamics (QED) and heavy quark systems. Participants seek advice on starting points for research and explore various theoretical frameworks and methodologies.
Participants express differing views on the implications of bound states for renormalization, particularly regarding the Lamb shift and the effectiveness of various theoretical approaches. The discussion does not reach a consensus on these points.
Some assumptions about the applicability of effective field theories and the specific conditions under which they operate remain unaddressed. The discussion includes references to specific papers and theories without resolving the mathematical intricacies involved.
Researchers and students interested in quantum field theory, particularly those focusing on bound states, renormalization techniques, and effective field theories in particle physics.
Thanks, I'm on it!john baez said:You could start with Chapter 10 of Itzykson and Zuber's Quantum Field Theory, which discusses renormalization for bound states, and then look at some of the papers they refer to.
The modern approach to QFT in bound states is through the use of effective field theories. For QED bound states, look for NRQED (non relativistic QED). Look for a paper on Lamb shift in NRQED to see the details. The renormalization is done as usual in an effective field theory, the bound state part shows up only in the fact that the asymptotic state is not free particles but a bound state, effectively one must sum up all the ladder Coulomb exchanges to infinity and this corresponds to the asymptotic state being a bound state satisfying Schrödinger's equation with a Coulomb potential. Again, see my paper on Lamb shift in NRQED for details on the Lamb shift calculation in this approach (look also for papers on "potential NRQED").Orion Pax said:When we are calculating the loop corrections in our theory (QED, for instance), how does the fact that our electron is in a bound state show itself in the renormalization? Does it matter at all? If so, then why are the predicted values for the Lamb shift, which are calculated in QFT for the electron in Hydrogen, i.e for a bound state, in such close agreement with experiment? Am I missing something here? Thanks