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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
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) ...
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Publisher Resources

ISBN: 9781466579897