This article is to be printed in 2012 but it is already available online at http://iopscience.iop.org/1751-8121/45/1/015305/.
Artilce details: S N Filippov and V I Man'ko 2012 J. Phys. A: Math. Theor. 45 015305
We develop a star-product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators, (a+)man. The corresponding phase space is a two-dimensional lattice with nodes (m,n) given by pairs of non-negative integers. The star-product kernel of symbols on the lattice and intertwining kernels to other schemes are found in an 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.