Characterization of Infrared Catastrophe by The Carleman Operator and Its Singularity

Details Characterization of Infrared Catastrophe by The Carleman Operator and Its Singularity Characterization of Infrared Catastrophe by The Carleman Operator and Its Singularity

2004-03-05

arxiv.org/abs/math-ph/0403008v6

Physics

Mathematical Physics

Title was chaged and some theorems were also revised

Scientific paper

This paper addresses some mathematical problems arising from the infrared (IR) catastrophe in quantum field theory. IR catastrophe is formulated and studied in operator theory, characterized by the Carleman operator. Non-existence of ground state under IR catastrophe is also investigated with the help of the characterization. The theory presented in this paper is applied to the Hamiltonian of the model describing a non-relativistic electron coupled with a quantum field of phonons or polaritons in the light of mathematics as well as solid state physics.

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