Schwinger’s oscillator realization of an SO(9) tensor operator

The weights and representation matrices of the vector and the spinor representation of the Lie algebra SO(9) are introduced in the quantum mechanical language. Tensor product decompositions of any two of them are explicitly shown by using an algebraic method of quantum mechanics. Similar decompositions are finally achieved for a coupled tensor operator in the picture of Schwingers bosonic oscillators.     

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.