Wick's theorem provides a connection between time ordered products of bosonic or fermionic fields, and their normal ordered counterparts. We consider a generic pair of operator orderings and we prove, by induction, the theorem that relates them. We name this the general Wick's theorem (GWT) because it carries Wick's theorem as special instance, when one applies the GWT to time and normal orderings. We establish the GWT both for bosonic and fermionic operators, i.e., operators that satisfy c-number commutation and anticommutation relations respectively. We remarkably show that the GWT is the same, independent of the type of operator involved. By means of a few examples, we show how the GWT helps treat demanding problems by reducing the amount of calculations required.Wick's theorem provides a connection between time ordered products of bosonic or fermionic fields, and their normal ordered counterparts. We consider a generic pair of operator orderings and we prove, by induction, the theorem that relates them. We name this the general Wick's theorem (GWT) because it carries Wick's theorem as special instance, when one applies the GWT to time and normal orderings. We establish the GWT both for bosonic and fermionic operators, i.e., operators that satisfy c-number commutation and anticommutation relations respectively. We remarkably show that the GWT is the same, independent of the type of operator involved. By means of a few examples, we show how the GWT helps treat demanding problems by reducing the amount of calculations required.

arXiv:2110.02920Physical Review ANov 15, 20219 citations

Commutation Relations

Brian P. Anderson

SPIE eBooksSep 12, 20190 citations

Perturbation theory for the spin- $frac12$ Heisenberg ferromagnet I. Wick's theorem and diagrammatic representationPerturbation theory for the spin-$frac12$ Heisenberg ferromagnet I. Wick's theorem and diagrammatic representation

Anna Kühnel

Pauli operators are treated as Bose operators fulfilling q -number commutation relations. An analogue of Wick's theorem for Pauli operators is formulated suitable for perturbation theory. The lowest-order contributions to the perturbation series for the temperature dependent one-particle causal Green function are calculated, and a diagrammatic representation is introduced for them. It is not necessary to have a different meaning of the same graph depending on the order of temperatures contained in it. The connected graphs representing the perturbation series up to second order are drawn explicitly.Pauli operators are treated as Bose operators fulfilling q -number commutation relations. An analogue of Wick's theorem for Pauli operators is formulated suitable for perturbation theory. The lowest-order contributions to the perturbation series for the temperature dependent one-particle causal Green function are calculated, and a diagrammatic representation is introduced for them. It is not necessary to have a different meaning of the same graph depending on the order of temperatures contained in it. The connected graphs representing the perturbation series up to second order are drawn explicitly.

Journal of Physics C Solid State PhysicsApr 1, 19698 citations

Perturbation theory for the spin-

frac12

Heisenberg ferromagnet I. Wick's theorem and diagrammatic representation