Star product and ordered moments of photon creation and annihilation operators
Sergey N. Filippov, Vladimir I. Man’ko · Journal of Physics A Mathematical and Theoretical · 2011
We develop a star-product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators, . 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.