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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
250 Commutation Relations, Normal Ordering, and Stirling Numbers
whereweusedthatforallβ F
+
β
(cF (c, c
)) one has :β:= (c
)
1
:β
:. This formal notation
means that the degree of the creation operator has to be decreased by one. This is possible
since, by definition, there is at least one singleton of type C in every β
, namely the one
which becomes “free” after deleting the edge in step (i) from above. Let us write, as above,
:β
:= (c
)
a
β
c
b
β
. Assuming for the moment that
βF
+
β
(cF (c,c
))
W
q
(β)=[a
β
]
q
W
q
(β
), (7.55)
we have, therefore, shown that
βF
+
(cF (c,c
))
W
q
(β):β:=
β
F (F (c,c
))
W
q
(β
)[a
β
]
q
(c
)
a
β
1
c
b
β
. (7.56)
Switching to the more convenient notation β
γ and inserting (7.54) and (7.56) into
(7.53) yields
γF (F (c,c
))
W
q
(γ)
'
q
a
γ
(c
)
a
γ
c
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Publisher Resources

ISBN: 9781466579897