Wave Function Renormalization for Particle-Field Interactions

TL;DR

This paper introduces a wave function renormalization scheme for non-relativistic particles interacting with quantum fields, addressing key issues in ultraviolet and infrared singularities within Hamiltonian models.

Contribution

It develops a new renormalization approach for Hamiltonian models, solving open problems related to singularities in the spin-boson and Nelson models.

Findings

Constructed the interacting Hamiltonian in ground state form

Resolved ultraviolet and infrared singularities

Established the role of infinite wave function renormalization

Abstract

In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the interacting Hamilton operator, in its ground state representation, for a large class of particle-field interactions; hereby addressing a number of open problems related to both ultraviolet and infrared singularities in the spin-boson and Nelson models, where the infinite wave function renormalization plays a fundamental role.