45 Pages
English

# Definition of the model

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45 Pages
English

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

Subjects

##### Physical system

Informations

Exrait

The infrared problem
Je´r´emy Faupin
Introduction
Deﬁnition of the model
Properties ofP7→ Eg(P)
Ground states of Hg(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→ Eg(P) Ground states of Hg(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 theHgcommutes with the total momentum operator For a ﬁxed total momentumP, we study the associated reduced HamiltonianHg(P)
Question Existence or non-existence of a ground state forHg(P): Is Eg(P) = infσ(Hg(P)) an eigenvalue ofHg(P)?
2 / 20
The infrared problem
J´er´emy Faupin
Introduction
Deﬁnition of the model
Properties ofP7→ Eg(P) Ground states of Hg(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 theHgcommutes with the total momentum operator For a ﬁxed total momentumP, we study the associated reduced HamiltonianHg(P)
Question Existence or non-existence of a ground state forHg(P): Is Eg(P) = infσ(Hg(P)) an eigenvalue ofHg(P)?
2 / 20
The infrared problem
J´er´emy Faupin
Introduction
Deﬁnition of the model
Properties ofP7→ Eg(P) Ground states of Hg(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:Hgcommutes with the total momentum operator For a ﬁxed total momentumP, we study the associated reduced HamiltonianHg(P)
Question Existence or non-existence of a ground state forHg(P): Is Eg(P) = infσ(Hg(P)) an eigenvalue ofHg(P)?
2 / 20