Double and dual numbers. SU(2) groups, two-component spinors and generating functions
Abstract We explicitly show that the groups of 2 × 2 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 ( 2 + 1 ) 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.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedad Mexicana de Física
2020
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| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2020000400418 |
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