Star product and ordered moments of photon creation and annihilation operators

Details Star product and ordered moments of photon creation and annihilation operators Star product and ordered moments of photon creation and annihilation operators

2011-08-10

arxiv.org/abs/1108.2244v3

J. Phys. A: Math. Theor. 45 (2012) 015305

Physics

Quantum Physics

14 pages, 4 figures, some misprints are corrected, to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/45/1/015305

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.

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