Definition of the model

Jérémy Faupin

Description

The infrared problem Jeremy Faupin Introduction Definition of the model Properties of P 7? Eg (P) Ground states of Hg (P) The infrared problem for the dressed non-relativistic electron Jeremy Faupin University of Bordeaux 1 March 11 2009, JSO, Institut Fourier Joint work with L. Amour, B. Grebert and J.-C. Guillot 1 / 20

• free electron


• spin neglected


• reduced hamiltonian


• inf ?


• jeremy faupin


• translation invariant


• hamiltonian hg


• physical system

Sujets

• Free electron model
• Translational symmetry
• Physical system

Informations

• Publié par: pefav
• Publié le: 01 novembre 2009
• Nombre de lectures: 19
• Langue: English

Extrait

The infrared problem

Je´r´emy Faupin

Introduction

Definition of the model

Properties ofP7→ E g (P)

Ground states of H g (P)

The

infrared

problem

for the dressed electron

Je´re´myFaupin

University of Bordeaux 1

non-relativistic

March 11 2009, JSO, Institut Fourier

Joint work with L.Amour,B.Gre´bertandJ.-C.Guillot

1 / 20

The infrared problem

J´er´emy Faupin

Introduction

Definition of the model

Properties ofP7→ E g (P) Ground states of H g (P)

Introduction

Physical system •1 free electron described by the parametersx,p,g,m •Spin neglected ¯ •Units:h=c= 1 •Non-relativistic electron •Interaction with the quantized electromagnetic field in the Coulomb gauge

Reduced Hamiltonian •The physical system is translation invariant: Hamiltonian theH g commutes with the total momentum operator •For a fixed total momentumP, we study the associated reduced HamiltonianH g (P)

Question Existence or non-existence of a ground state forH g (P): Is E g (P) = infσ(H g (P)) an eigenvalue ofH g (P)?

2 / 20

The infrared problem

J´er´emy Faupin

Introduction

Definition of the model

Properties ofP7→ E g (P) Ground states of H g (P)

Introduction

Physical system •1 free electron described by the parametersx,p,g,m •Spin neglected ¯ •Units:h=c= 1 •Non-relativistic electron •Interaction with the quantized electromagnetic field in the Coulomb gauge

Reduced Hamiltonian •The physical system is translation invariant: Hamiltonian theH g commutes with the total momentum operator •For a fixed total momentumP, we study the associated reduced HamiltonianH g (P)

Question Existence or non-existence of a ground state forH g (P): Is E g (P) = infσ(H g (P)) an eigenvalue ofH g (P)?

2 / 20

The infrared problem

J´er´emy Faupin

Introduction

Definition of the model

Properties ofP7→ E g (P) Ground states of H g (P)

Introduction

Physical system •1 free electron described by the parametersx,p,g,m •Spin neglected ¯ •Units:h=c= 1 •Non-relativistic electron •Interaction with the quantized electromagnetic field in the Coulomb gauge

Reduced Hamiltonian • Hamiltonian theThe physical system is translation invariant:H g commutes with the total momentum operator •For a fixed total momentumP, we study the associated reduced HamiltonianH g (P)

Question Existence or non-existence of a ground state forH g (P): Is E g (P) = infσ(H g (P)) an eigenvalue ofH g (P)?

2 / 20