"This thesis is devoted to the study of two nonlinear relativistic quantum models. In the first part, we prove by a perturbation method the existence of solutions of the coupled Einstein–Dirac–Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and for a weak electromagnetic coupling. In the second part, we study a relativistic mean-field model that describes the behavior of nucleons in the atomic nucleus. We provide a condition that ensures the existence of a ground state solution of the relativistic mean-field equations in a static case; in particular, we relate the existence of critical points of a strongly indefinite energy functional to strict concentration-compactness inequalities.

Etude mathematique de modèles non linéaires issus de la physique quantique relativiste.

ROTA NODARI, SIMONA
2011

Abstract

"This thesis is devoted to the study of two nonlinear relativistic quantum models. In the first part, we prove by a perturbation method the existence of solutions of the coupled Einstein–Dirac–Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and for a weak electromagnetic coupling. In the second part, we study a relativistic mean-field model that describes the behavior of nucleons in the atomic nucleus. We provide a condition that ensures the existence of a ground state solution of the relativistic mean-field equations in a static case; in particular, we relate the existence of critical points of a strongly indefinite energy functional to strict concentration-compactness inequalities.
6-lug-2011
Francese (Altre)
RUF, BERNHARD
PELOSO, MARCO MARIA
Università degli Studi di Milano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14242/77197
Il codice NBN di questa tesi è URN:NBN:IT:UNIMI-77197