Double and dual numbers. SU(2) groups, two-component spinors and generating functions
Keyword(s):
We explicitly show that the groups of $2 \times 2$ 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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2007 ◽
Vol 463
(2085)
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pp. 2329-2350
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1980 ◽
Vol 83
(2)
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pp. 234-246
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2008 ◽
Vol 17
(4)
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pp. 619-625
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1956 ◽
Vol 8
◽
pp. 256-262
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1993 ◽
Vol 304
(3-4)
◽
pp. 256-262
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Keyword(s):
2007 ◽
Vol 463
(2081)
◽
pp. 1199-1210
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