What is "dressed particle" approach to QFT?
Recall our discussion of the QED Hamiltonian where we found that the presence of terms like a*c*a makes this Hamiltonian useless for studying the time evolution. The problem was that these terms act non-trivially on 1-particle states. The main idea of the "dressed particle" approach is that there can be no interaction in the vacuum state and in 1-particle states. These states should evolve in time as if there were no interaction at all. Mathematically this requirement means that all terms in the interaction Hamiltonian should have at least two annihilation operators. In order to maintain the Hermiticity, there should be at least two creation operators in each interaction term. So, in a theory of interacting electrons and photons, the simplest normally ordered terms allowed in the interaction Hamiltonian are
The first term here describes a direct electron-electron interaction; the second term is an electron-photon potential responsible for the Compton scattering; the third term describes bremsstrahlung, i.e., emission of photons in electron-electron collisions; the fourth term is a three-body electron-electron-electron potential,...
It is important that all these terms yield zero when acting on the vacuum and 1-particle states. This means, for example, that the electron mass is not affected by interaction, so there is no need for renormalization.
As I mentioned here , a number of relativistically invariant and cluster separable models of this sort were constructed by H. Kita. There is also a "dressing approach" by Greenberg and Schweber which allows one to make a "dressed particle" theory out of virtually any usual QFT. What is really exciting is that this approach works and one can construct a "dressed" version of QED and other popular theories. This provides a completely new perspective on foundations of relativistic quantum physics.