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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
Appendix E
The Baker–Campbell–Hausdorff Formula
A problem which often occurs in applications and in the study of Lie groups and Lie
algebras (see Appendix D) is that of expressing the product of two exponential operators
in an equivalent form. Clearly, if the operators X and Y commute, that is, [X, Y ]=0,then
e
X
e
Y
= e
X+Y
,wheree
X
=exp(X) is defined by the usual power series. The generalization
of this formula to the case when X and Y do not commute is the content of the Baker–
Campbell–Hausdorff formula. To formulate the theorem, we introduce a concise notation
for nested commutators (or brackets). Thus, we abbreviate
[X, [X,...,[X
! "
r
1
, [Y,[Y,...,[Y
! ...
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Publisher Resources

ISBN: 9781466579897