# Operator-theoretic infrared renormalization and construction of dressed 1-particle states

@inproceedings{Chen2001OperatortheoreticIR, title={Operator-theoretic infrared renormalization and construction of dressed 1-particle states}, author={Thomas Chen}, year={2001} }

We consider the infrared problem in a model of a freely propagating, nonrelativistic charged particle of mass 1 in interaction with the quantized electromagnetic field. The hamiltonian of the system is regularized by an infrared cutoff $\ssig\ll 1$ and an ultraviolet cutoff $\Lambda\sim 1$ in the interaction term, in units of the mass of the charged particle. Due to translation invariance, it suffices to study $\Hps$, the restriction of the hamiltonian to the fibre Hilbert space of the…

## 47 Citations

### Mass Renormalization in Non-relativistic Quantum Electrodynamics with Spin 1/2

- Physics
- 2004

The effective mass $\mass$ of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff $\Lambda$ and the bare mass $m$ in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of…

### Mass Renormalization and Energy Level Shift in Non-Relativistic QED

- Physics
- 2002

Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized…

### Operator-theoretic renormalization group and aspects of the infrared problem in non-relativistic QED

- Physics
- 2003

One of the key difficulties in the study of non-relativistic QED is the appearance of infrared singularities in the computation of many fundamentally important quantities, such as scattering…

### Quasi-static Limits in Nonrelativistic Quantum Electrodynamics

- Physics
- 2008

Abstract.We consider a system of N nonrelativistic particles of spin 1/2 interacting with the quantized Maxwell field (mass zero and spin one) in the limit when the particles have a small…

### Infrared renormalization in non-relativistic QED for the endpoint case

- Physics, Mathematics
- 2006

We consider a spin 1 2 electron in a translation-invariant model of non-relativistic Quantum Electrodynamics (QED). Let H(~ p, σ) denote the fiber Hamiltonian corresponding to the conserved momentum…

### Spectral Analysis of the Dirac Polaron

- Mathematics
- 2006

A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by $H = \alpha\cdot(\hat\mathbf{p}-q\mathbf{A}(\hat\mathbf{x}))+m\beta + H_f$…

### Functional Integral Representation of the Pauli-Fierz Model with Spin 1/2

- Mathematics
- 2007

A Feynman-Kac-type formula for a L\'evy and an infinite dimensional Gaussian random process associated with a quantized radiation field is derived. In particular, a functional integral representation…

### Coherent infrared representations in non-relativistic QED

- Physics
- 2006

We consider dressed 1-electron states in a translation-invariant model of non-relativistic QED. To start with a well-defined model, the interaction Hamiltonian is cutoff at very large photon energies…

## 20 References

### On the Existence of Ground States for Massless Pauli-Fierz Hamiltonians

- Physics
- 2000

We consider in this paper the problem of the existence of a ground state for a class of Hamiltonians used in physics to describe a confined quantum system (”matter”) interacting with a massless…

### Asymptotic Electromagnetic Fields in Models of Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

- Physics
- 2000

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic…

### Renormalization Group Analysis of Spectral Problems in Quantum Field Theory

- Physics
- 1998

Abstract In this paper we present a self-contained and detailed exposition of the new renormalization group technique proposed in [1, 2]. Its main feature is that the renormalization group…

### Asymptotic Completeness for Rayleigh Scattering

- Physics
- 2001

Abstract. It is expected that the state of an atom or molecule, initially put into an excited state with an energy below the ionization threshold, relaxes to a ground state by spontaneous emission of…

### ON THE SCATTERING THEORY OF MASSLESS NELSON MODELS

- Mathematics
- 2002

We study the scattering theory for a class of non-relativistic quantum field theory models describing a confined non-relativistic atom interacting with a massless relativistic bosonic field. We…

### QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES

- Physics
- 1998

Abstract We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we…

### The Infrared Behaviour in Nelson's Model of a Quantum Particle Coupled to a Massless Scalar Field

- Physics
- 2000

Abstract. We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not…

### Ground state of the massless Nelson model without infrared cutoff in a non-Fock representation

- Physics, Mathematics
- 2000

We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical…

### Ground states in non-relativistic quantum electrodynamics

- Physics
- 2000

Abstract.The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state – one…