  We develop a star-product scheme of symbols defined by the normally ordered
powers of the creation and annihilation photon operators, (a\dag)^m a^n. The
corresponding phase space is a two-dimensional lattice with nodes (m,n) given
by pairs of nonnegative integers. The star-product kernel of symbols on the
lattice and intertwining kernels to other schemes are found in explicit form.
Analysis of peculiar properties of the star-product kernel results in new sum
relations for factorials. Advantages of the developed star-product scheme for
describing dynamics of quantum systems are discussed and time evolution
equations in terms of the ordered moments are derived.
