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Revista mexicana de física
versión impresa ISSN 0035-001X
Resumen
TORRES DEL CASTILLO, G.F. y GUTIERREZ-HERRERA, K.C.. Double and dual numbers. SU(2) groups, two-component spinors and generating functions. Rev. mex. fis. [online]. 2020, vol.66, n.4, pp.418-423. Epub 31-Ene-2022. ISSN 0035-001X. https://doi.org/10.31349/revmexfis.66.418.
We explicitly show that the groups of unitary matrices with determinant equal to 1 whose entries are double or dual numbers are homomorphic to ${\rm SO}(2,1)$ or to the group of rigid motions of the Euclidean plane, respectively, and we introduce the corresponding two-component spinors. We show that with the aid of the double numbers we can find generating functions for separable solutions of the Laplace equation in the Minkowski space, which contain special functions that also appear in the solution of the Laplace equation in the three-dimensional Euclidean space, in spheroidal and toroidal coordinates.
Palabras llave : Double numbers; dual numbers; unitary groups; spinors; Minkowski (2 + 1) space; Laplace’s equation; spheroidal coordinates; toroidal coordinates.