This thesis is motivated by questions arising in the eld of Mathematical Quantum Electrodynamics, the attempt of a proper mathematical description of Quantum Electrodynamics (QED). QED is the relativistic quantum eld theory of electrodynamics, which uni es Quantum Mechanics and Special Relativity in a consistent manner. From the mathematical point of view, QED is an abelian gauge theory with the symmetry group U(1) (phase factors) and the gauge eld mediating the interaction between the charged spin-1/2 elds is the electromagnetic eld. Aim of this thesis is the renormalization of the regularized relativistic electron positron eld together with a Coulomb interaction. The idea of the renormalization procedure is to compare the normal-ordered Hamiltonian with the original one. Choosing a conventional normal ordering, the change in Hamiltonian is given by a quadratic term. The choice of a suitable normal ordering amounts in a non-perturbative rede nition of the electron/positron states. This allows for the interpretation of change in the Hamiltonian as a certain renormalization. The proper interpretation of this renormalization and the various implications are discussed at the end.

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Bachelor Thesis from the year 2011 in the subject Mathematics - Miscellaneous, grade: 1,0, Technical University of Munich, language: English, abstract: This thesis is motivated by questions arising in the eld of Mathematical Quantum Electrodynamics, the attempt of a proper mathematical description of Quantum Electrodynamics (QED). QED is the relativistic quantum eld theory of electrodynamics, which uni es Quantum Mechanics and Special Relativity in a consistent manner. From the mathematical point of view, QED is an abelian gauge theory with the symmetry group U(1) (phase factors) and the gauge eld mediating the interaction between the charged spin-1/2 elds is the electromagnetic eld. Aim of this thesis is the renormalization of the regularized relativistic electron positron eld together with a Coulomb interaction. The idea of the renormalization procedure is to compare the normal-ordered Hamiltonian with the original one. Choosing a conventional normal ordering, the change in Hamiltonian is given by a quadratic term. The choice of a suitable normal ordering amounts in a non-perturbative rede nition of the electron/positron states. This allows for the interpretation of change in the Hamiltonian as a certain renormalization. The proper interpretation of this renormalization and the various implications are discussed at the end.