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 nonlinear Hartree dynamics can be seen as a subset of the diagrams arising in the time evolution of a Bose gas.

Friedrichs diagrams: bosonic and fermionic / M. Brooks, S. Lill. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 113:5(2023 Sep 16), pp. 101.1-101.26. [10.1007/s11005-023-01715-6]

Friedrichs diagrams: bosonic and fermionic

S. Lill
2023

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 nonlinear Hartree dynamics can be seen as a subset of the diagrams arising in the time evolution of a Bose gas.
Friedrichs diagrams; Many-body physics; Quantum field theory; Hartree equation; Feynman diagrams
Settore MAT/07 - Fisica Matematica
   The Mathematics of Interacting Fermions (FermiMath)
   FermiMath
   EUROPEAN COMMISSION
   101040991
16-set-2023
21-ago-2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1025553
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