Pauli-Fierz model with Kato-class potentials and exponential decays

TL;DR

This paper studies a generalized Pauli-Fierz Hamiltonian with Kato-class potentials in quantum electrodynamics, proving exponential decay of bound states and uniqueness of the ground state using path measure techniques.

Contribution

It introduces a new class of Hamiltonians with Kato-class potentials and establishes exponential decay and uniqueness results through a path measure approach.

Findings

Bound states decay exponentially in space

Ground state is unique

Hamiltonian is well-defined as a self-adjoint operator

Abstract

Generalized Pauli-Fierz Hamiltonian with Kato-class potential $\KPF$ in nonrelativistic quantum electrodynamics is defined and studied by a path measure. $\KPF$ is defined as the self-adjoint generator of a strongly continuous one-parameter symmetric semigroup and it is shown that its bound states spatially exponentially decay pointwise and the ground state is unique.