Effective dynamics of an electron coupled to an external potential in non-relativistic QED

Volker Bach (1) , Thomas Chen (2) , Jérémy Faupin (3) , Jürg Fröhlich (4) , Israel Michael Sigal (5)

1 IAA - Institut for Analysis and Algebra
2 University of Texas at Austin [Austin]
3 IMB - Institut de Mathématiques de Bordeaux
4 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]
5 University of Toronto

In the framework of non-relativistic QED, we show that the renormalized mass of the electron (after having taken into account radiative corrections) appears as the kinematic mass in its response to an external potential force. Specifically, we study the dynamics of an electron in a slowly varying external potential and with slowly varying initial conditions and prove that, for a long time, it is accurately described by an associated effective dynamics of a Schrodinger electron in the same external potential and for the same initial data, with a kinetic energy operator determined by the renormalized dispersion law of the translation-invariant QED model.

Domaines: Physique mathématique [math-ph]

Volker Bach, Thomas Chen, Jérémy Faupin, Jürg Fröhlich, Israel Michael Sigal. Effective dynamics of an electron coupled to an external potential in non-relativistic QED. Annales Henri Poincaré, 2013, 14 (6), pp.1573-1597. ⟨10.1007/s00023-012-0222-8⟩. ⟨hal-01279972⟩