R D Mota et al 2004 J. Phys. A: Math. Gen. 37 2835 doi:10.1088/0305-4470/37/7/022
R D Mota1, M A Xicoténcatl2 and V D Granados3
Show affiliationsIn this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan–Schwinger map of a triplet of harmonic oscillators with the Gell–Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan–Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell–Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
Issue 7 (20 February 2004)
Received 3 July 2003
Published 4 February 2004
R D Mota et al 2004 J. Phys. A: Math. Gen. 37 2835
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