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A SPECTRUM OF THE DIRAC OPERATOR WITH AN EXTERNAL YANG-MILLS GAUGE FIELD ON DE SITTER SPACE // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 25-27

The Dirac operator with an external Yang–Mills gauge field is considered on de Sitter space in terms of a noncommutative integration method related to the orbit method in the Lie group theory. A Yang–Mills field is presented for which the de Sitter group serves as the symmetry group of the Dirac operator. A spectrum of the Dirac operator with the Yang–Mills field is calculated in explicit form.

Keywords: the Dirac equation, noncommutative integration, de Sitter space