2011/08/31 by S. N. Filippov, S N Filippov, V. I. Man'ko +1
Computer Science · Mathematics · Physics and Astronomy · #Annihilation #Creation and annihilation operators #Kernel (algebra) #Lattice (music) #Phase space #Photon #Product (mathematics) #Quantum #Quantum Information and Cryptography #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/45/1/015305
published as J. Phys. A: Math. Theor. 45 (2012) 015305 · 14 pages, 4 figures, some misprints are corrected, to appear in J. Phys. A
arxiv created 2011/11/21 · openalex publication_date 2011/12/01 · arxiv updated 2012/01/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.