Geodesic
Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states
Documenta mathematica, Tome 18 (2013), pp. 1481-1519.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 81V10, 81L05, 46T99
Keywords: Pauli-Fierz model, quasifree states, mass renormalization, minimization techniques 
@article{DOCMA_2013__18__a4,
     author = {Bach, Volker and Breteaux, S\'ebastien},
     title = {Minimization of the energy of the nonrelativistic one-electron {Pauli-Fierz} model over quasifree states},
     journal = {Documenta mathematica},
     pages = {1481--1519},
     publisher = {mathdoc},
     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a4/}
}
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Bach, Volker; Breteaux, Sébastien. Minimization of the energy of the nonrelativistic one-electron Pauli-Fierz model over quasifree states. Documenta mathematica, Tome 18 (2013), pp. 1481-1519. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a4/