Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference31 articles.
1. Friedrichs, K.O.: Perturbation of Spectra in Hilbert Space. American Mathematical Society, Providence (1965)
2. Hepp, K.: Théorie de la Renormalisation. Springer, Berlin (1969)
3. Glimm, J.: Boson fields with the: $$\Phi ^4$$: interaction in three dimensions. Commun. Math. Phys. 10, 1–47 (1968)
4. Glimm, J., Jaffe, A.: Positivity of the $$ \varphi _3^4 $$ Hamiltonian. Fortschr. Phys. 21, 327–376 (1973)
5. Feldman, J.S., Osterwalder, K.: The Wightman axioms and the mass gap for weakly coupled $$ (\varphi ^4)_3 $$ quantum field theories. Ann. Phys. 97(1), 80–135 (1976)