2020/05/13 by Thomas Forrest Kieffer, Kieffer, Thomas Forrest
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical mechanics #Connection (principal bundle) #Electromagnetic field #Electron #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics #Maxwell's equations #Numerical methods in inverse problems #Pauli exclusion principle #Physics #Quantum #Quantum electrodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Work (physics) #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.2005.06556
published in arXiv (Cornell University) (Cornell University) · 95 pages. PhD thesis, Georgia Institute of Technology, May 2020. Includes results from arXiv:1904.06748
arxiv created 2020/05/13 · openalex publication_date 2020/05/13 · arxiv updated 2020/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the quantum mechanical many-body problem of N ≥ 1 non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and K ≥ 0 static nuclei. We model the dynamics of the electrons and their self-generated electromagnetic field using the so-called many-body Maxwell-Pauli equations. The main result of this thesis is to construct time global, finite-energy, weak solutions to the many-body Maxwell-Pauli equations under the assumption that the fine structure constant α and the nuclear charges are not too large. The assumptions on the size of α and the nuclear charges ensure that we have energetic stability for this system, i.e., the absolute ground state energy exists. The work in this thesis serves as an initial step towards understanding the connection between the energetic stability of matter in quantum mechanics and the well-posedness of the corresponding dynamical equations.