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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 8
A Generalization of the Weyl Algebra
In this chapter we introduce a generalization of the Weyl algebra and consider some related
combinatorial structures, in particular, associated generalized Stirling and Bell numbers.
Recall that we considered in Chapters 5 and 6 the Weyl algebra A
h
defined by two generators
U and V satisfying
UV VU = h
for some h C. In Chapter 7 we considered three variants of it: 1) the q-deformed Weyl
algebra A
h|q
where UV qV U = h, 2) the meromorphic Weyl algebra MA
h
where UV
VU = hV
2
,and3)theq-deformed meromorphic Weyl algebra MA
h|q
where UV qV U =
hV
2
. As a common generalization, we will introduce in Chapter 9
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Publisher Resources

ISBN: 9781466579897