Nonlinear Phenomena in Complex Systems, 2012, Vol.15, No.3, pp.241-252

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2012, Vol.15, No.3, pp.241-252

Spin 1 Particle on 4-Dimensional Sphere: Extended Helicity Operator, Separation of Variables, and Exact Solutions.
V. Red'kov, E. Ovsiyuk, and V.V. Kisel

Spin 1 particle is investigated in 3-dimensional curved space of constant positive curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin-Kemmer equation in quasi cylindrical coordinates. The problem is solved exactly in hypergeometric functions, the energy spectrum determined by three discrete quantum numbers is obtained. Transition to a massless case of electromagnetic field is performed.

Key words: spaces of constant curvature, electromagnetic field, separation of variables, Duffin-Kemmer equation, extended helicity operator

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