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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
Chapter 9
The q-Deformed Generalized Weyl Algebra
In this chapter a q-deformation of the generalized Weyl algebra A
s;h
defined in Chapter 8
is introduced. Its generators U and V satisfy UV qV U = hV
s
, and it will be denoted
by A
s;h|q
. As in the preceding chapters, we will be interested in ordering results for words
in the generators U and V . In particular, we introduce associated q-deformed generalized
Stirling and Bell numbers and derive some of their properties. As it will turn out, the study
of A
s;h|q
is significantly more difficult than the undeformed case, and explicit expressions
will be given only for special cases. As in the undeformed case we ...
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Publisher Resources

ISBN: 9781466579897