Friedrichs Diagrams -- Bosonic and Fermionic

Abstract

We give a mathematically precise review of a diagrammatic language introduced by Friedrichs in order to simplify computations with creation and annihilation operator products. In that language, we establish explicit formulas and algorithms for evaluating bosonic and fermionic commutators. Further, as an application, we demonstrate that the non-linear Hartree dynamics can be seen as a subset of the diagrams arising in the time evolution of a Bose gas.

26 pages, 11 figures. An important typo in Theorem 2.3, (23) has been fixed with respect to the previous version

References in corpus (3)

• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Correlation Energy of a Weakly Interacting Fermi Gas
• The dilute Fermi gas via Bogoliubov theory

Cited by in corpus (1)

• Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams