A Mathematical Mechanism of Infrared Catastrophe

Abstract

We derive a mathematical mechanism of infrared catastrophe from the idea for the proof in [22, 23] and generalize it so that we can apply it to several models in quantum field theory. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by the Carleman operator, we study the mechanism of infrared catastrophe. And moreover, based on the mechanism, we show some proofs of absence of ground state.

Cite this paper

@inproceedings{Hirokawa2004AMM, title={A Mathematical Mechanism of Infrared Catastrophe}, author={Masao Hirokawa}, year={2004} }