Nöth, Markus Hartmut (2021): On relativistic interaction of electric charges and external fields in quantum electrodynamics. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

PDF
Noeth_Markus_Hartmut.pdf 1MB 
Abstract
The main subject of this thesis is the problem of introducing interactions into relativistic quantum mechanics. This problem has many facets, two of which will be discussed. The first one deals with a recent relativistically invariant integral equation for multitime wave functions by Lienert. From a mathematical point of view this proposal is promising, since variants of it have been shown to be mathematically welldefined. In this thesis, firstly, previous results on existence and uniqueness of solutions of a variant of this equation for scalar particles are extended to include more realistic types of interaction. Secondly, a proof of existence and uniqueness of solutions of another variant that allows to treat spin 1/2 particles is provided. The second facet concerns interactions in the context of a variable number of particles. Following famous works of Dirac, Feynman and Schwinger, we treat external electrodynamic fields in an otherwise free Quantum Field Theory of electrons. In previous results, candidates for the time evolution operator have been constructed in this setting. This construction is unique up to a phase, which may depend on the external field. This phase affects the charge current density and should thus be identified. In this work, this problem is addressed by a geometric, which was inspired by and developed jointly with my supervisors, construction assuming a certain causality condition. Secondly, a compact formula for the scattering operator in terms of the corresponding oneparticle scattering operator is provided and shown to be welldefined, assuming certain conditions on the external field. This formula is used to show that the second quantized scattering operator is an analytic function of the external field in a certain sense.
Item Type:  Theses (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date of oral examination:  26. November 2021 
1. Referee:  Deckert, DirkAndré 
MD5 Checksum of the PDFfile:  74388f3f13d542d271eee179ff77718d 
Signature of the printed copy:  0001/UMC 28619 
ID Code:  29250 
Deposited On:  09. Mar 2022 09:58 
Last Modified:  09. Mar 2022 09:59 