Geodesic
Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states
Documenta mathematica, Tome 18 (2013), pp. 1481-1519
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

In this article the existence of a minimizer for the energy for the nonrelativistic one-electron Pauli-Fierz model within the class of quasifree states is established. To this end it is shown that the minimum of the energy on quasifree states coincides with the minimum of the energy on pure quasifree states, where existence and uniqueness of a minimizer holds. Infrared and ultraviolet cutoffs are assumed, along with sufficiently small coupling constant and momentum of the dressed electron. A perturbative expression of the minimum of the energy on quasifree states for a small momentum of the dressed electron and small coupling constant is given. We also express the Lagrange equation for the minimizer in terms of the generalized one particle density matrix of the pure quasifree state.
DOI : 10.4171/dm/434
Classification : 46T99, 81V10
Mots-clés : quasifree states, Pauli-Fierz model, mass renormalization, minimization techniques 
@article{10_4171_dm_434,
     author = {Volker Bach and S\'ebastien Breteaux and Tim Tzaneteas},
     title = {Minimization of the energy of the nonrelativistic one-electron {Pauli-Fierz} model over quasifree states},
     journal = {Documenta mathematica},
     pages = {1481--1519},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/434},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/434/}
}
TY  - JOUR
AU  - Volker Bach
AU  - Sébastien Breteaux
AU  - Tim Tzaneteas
TI  - Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states
JO  - Documenta mathematica
PY  - 2013
SP  - 1481
EP  - 1519
VL  - 18
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/434/
DO  - 10.4171/dm/434
ID  - 10_4171_dm_434
ER  - 
%0 Journal Article
%A Volker Bach
%A Sébastien Breteaux
%A Tim Tzaneteas
%T Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states
%J Documenta mathematica
%D 2013
%P 1481-1519
%V 18
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/434/
%R 10.4171/dm/434
%F 10_4171_dm_434
Volker Bach; Sébastien Breteaux; Tim Tzaneteas. Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states. Documenta mathematica, Tome 18 (2013), pp. 1481-1519. doi: 10.4171/dm/434

Cité par Sources :