
Chapter 5
The Weyl Algebra, Quantum Theory, and
Normal Ordering
This chapter focuses on the Weyl algebra and the process of normal ordering words in its
generators. We consider an “abstract” version of the Weyl algebra which is characterized
by two generators U and V satisfying the commutation relation UV − VU = h for some
h ∈ C. More precisely, on the right-hand side of the commutation relation one has hI
where I denotes the identity commuting with U and V (hence, with all words in U and V ).
However, we identify cI with c, and since we are interested in the combinatorial consequences
of the commutation relation this makes no difference. In Chapter