On integrating out short-distance physics

TL;DR

The paper demonstrates that in certain atomic scattering problems, short-distance physics can be integrated out naturally within perturbative calculations, leading to inherent soft inelastic processes and inclusive cross-sections, suggesting a similar approach for QFT.

Contribution

It shows that short-distance physics can be automatically integrated out in specific atomic scattering models, proposing a new formulation approach for quantum field theory.

Findings

Soft inelastic processes occur at the first Born approximation

Inclusive cross-sections are inherent from the start

Short-distance physics integration can be automatic without renormalization

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.