
Normal Ordering in the Weyl Algebra – Further Aspects 203
Theorem 6.43 (Wick’s theorem) Let F (U, V ) be a polynomial or formal series in the
generators of the extended Weyl algebra
ˆ
A
1
. Its normal ordered form F
(n)
(U, V ) can be
written as
F
(n)
(U, V )=
π∈C(F (U,V ))
:π: .
Wick’s theorem was first formulated by Wick [1140] in 1950 in the context of quantum
field theory
11
(see Section 5.2.7.7 and the end of Section 5.3.3). Here one is interested in
expressing a time-ordered product of operators in terms of normal ordered operators. The
contraction of a field operator and its adjoint is the only nonvanishing contraction and gives
rise to propagators; see (5.78) ...