The Correlation Energy of Many-Body Fermi Systems (A05)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 470903074

We study the correlation energy of fermions, defined as the difference between the ground state energy of the many-body state and the Hartree-Fock energy. The goal is to provide a rigorous derivation of two formulas: (i) the Gell-Mann--Brueckner formula for the energy of jellium at high density, and (ii) the Huang–Yang formula for the energy of low-density Fermi gas with short-range repulsive interactions. These long-standing open problems will be addressed by a rigorous implementation of Bogolubov theory and its refinements for Fermi systems.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 352: Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
• International Connection: Austria
• Applicant Institution: Ludwig-Maximilians-Universität München
• Project Heads: Professor Dr. Christian Hainzl; Professor Dr. Phan Thanh Nam; Professor Dr. Robert Seiringer