
Chapter 6
Normal Ordering in the Weyl Algebra –
Further Asp ects
This chapter continues the study of normal ordering in the Weyl algebra which we began
in Chapter 5. In Section 6.1, normal ordering in the “abstract” Weyl algebra (generated by
generators U and V satisfying UV − VU = h) is treated and many results are collected,
some of which were already discussed in preceding chapters. Among the results we discuss
are Viskov’s identity, the connection of normal ordering to rook numbers and the identity of
Bender, Mead, and Pinsky. Turning to the extended Weyl algebra – allowing formal series
in the generators –, several classical results (due to Cr