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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
164 Commutation Relations, Normal Ordering, and Stirling Numbers
where {C, D} = CD + DC denotes the anticommutator.Furthermore,ifwedenoteby
ˆn
F
=
ˆ
f
ˆ
f the fermionic number operator, then one has n
F
,
ˆ
f
]=
ˆ
f
as well as n
F
,
ˆ
f]=
ˆ
f.
Note that the above relations imply, in particular, (
ˆ
f
)
2
= 0. If we denote the ground state
defined by
ˆ
f|0 =0–by|0, then we generate all other states by the action of
ˆ
f
. However,
due to (
ˆ
f
)
2
= 0 the state |1 is the only nontrivial state! Thus, the fermionic Fock space is
only two-dimensional (hence, isomorphic to C
2
). The operators
ˆ
f
and
ˆ
f can, therefore, be
represented by complex 2 ×2 matrices.
Remark 5.23 The ene ...
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Publisher Resources

ISBN: 9781466579897