Minimization of an Energy Functional for an Electron in the quantized Radiation Field over quasifree States

Abstract

Building upon the works of Bach, Breteaux, and Tzaneteas (2013) and of Bach and Hach (2022), the Bogolubov-Hartree-Fock (BHF) energy of the Pauli-Fierz Hamiltonian is investigated. Upper and lower bounds on the BHF energy are derived, which suggest positivity of the minimizer, see Theorem IV.6. Under the assumption that the minimizer is indeed positive, a necessary condition on the minimizer is determined by introducing a parameterization, which simplifies the functions of operators appearing in the energy functional.

47 pages, thesis supervised by Volker Bach. This is my thesis, handed in on April 24, 2023 as part of the Master of Science program in mathematics at the TU Braunschweig