Modulo the ideal generated by the derivative fields, the normal ordered
product of holomorphic fields in two-dimensional conformal field theory yields
a commutative and associative algebra. The zero mode algebra can be regarded as
a deformation of the latter. Alternatively, it can be described as an
associative quotient of the algebra given by a modified normal ordered product.
We clarify the relation of these structures to Zhu's product and Zhu's algebra
of the mathematical literature.Comment: LaTeX (BibTeX), 6 pages, no figure
