  We describe an algebra G of diagrams which faithfully gives a diagrammatic
representation of the structures of both the Heisenberg-Weyl algebra H - the
associative algebra of the creation and annihilation operators of quantum
mechanics - and U(L_H), the enveloping algebra of the Heisenberg Lie algebra
L_H. We show explicitly how G may be endowed with the structure of a Hopf
algebra, which is also mirrored in the structure of U(L_H). While both H and
U(L_H) are images of G, the algebra G has a richer structure and therefore
embodies a finer combinatorial realization of the creation-annihilation system,
of which it provides a concrete model.
