I submitted an article with simple calculations where the "short-distance physics" is integrated out automatically rather than "manually". http://arxiv.org/abs/1409.8326
Happy reading!
Abstract:
I consider a special atomic scattering problem where the target atom has
distinct “soft” and “hard” excitation modes. I demonstrate that in this
problem the integration out of “short-distance” (or “high-energy”)
physics may occur automatically in the regular perturbative
calculations, i.e., it may occur without any cut off and
renormalization. Not only that, the soft inelastic processes happen
already in the first Born approximation and the inclusive cross-sections
become unavoidable from the very beginning. All that is possible
because of correct physical and mathematical formulation of the problem.
I propose to build QFT in a similar way.
P.S. I updated the article, mainly with writing an Appendix to address the mixed variables and the Hamiltonian splitting.
P.P.S. Now it's been published online: http://www.aiscience.org/journal/paperInfo/pj?paperId=2156
