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 Schrodinger'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
The concept of renormalization in QFT refers to a mathematical technique used to remove infinite values in certain calculations. These infinite values arise in quantum theories due to the interaction between particles and the vacuum. Renormalization allows for the calculation of observable quantities in a more meaningful and finite way.
In the context of bound states, renormalization is used to remove the infinite self-energy of the bound state. This self-energy arises from the interaction between the bound state and the vacuum. By applying renormalization, the bound state's mass and energy can be calculated in a more accurate and finite manner.
Renormalization is a crucial aspect of QFT as it allows for the calculation of meaningful and finite quantities. Without renormalization, the infinite values that arise in quantum theories would render many calculations meaningless. Additionally, renormalization has been successful in predicting and explaining experimental results in particle physics.
The renormalization process alters the behavior of bound states in QFT by removing the infinite self-energy of the bound state. This results in a more accurate and finite calculation of the bound state's mass and energy. Additionally, renormalization can also reveal important information about the bound state's interactions with other particles and the vacuum.
Yes, renormalization can be applied to all types of bound states in QFT. It is a fundamental technique used to remove infinite values and calculate meaningful quantities in quantum theories. Whether the bound state is composed of fundamental particles or composite particles, renormalization is an essential tool for understanding their behavior and interactions.