We consider arbitrary splits of field operators into two parts; ψ=ψ++ψ−, and use the corresponding definition of normal ordering introduced earlier [T. S. Evans and D. A. Steer, Nucl. Phys. B 474, 481 (1996)]. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick’s theorem. Despite this, we prove that Wick’s theorem still holds in its usual form as long as the contraction is a c-number. Wick’s theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.
Gian Carlo Wick (15 October 1909 – 20 April 1992) was an Italian theoretical physicist who made important contributions to quantum field theory. The Wick rotation, Wick contraction, Wick's theorem, and the Wick product are named after him.
Gian Carlo Wick (15 October 1909 – 20 April 1992) was an Italian theoretical physicist who made important contributions to quantum field theory. The Wick rotation, Wick contraction, Wick's theorem, and the Wick product are named after him.
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, independently from the type of operator involved. By means of a few examples, we show how the GWT helps treating demanding problems by reducing the amount of calculations required.
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