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Abstract: (Springer)
We study the Weyl algebra A pertaining to a particle constrained on a sphere, which is generated by the coordinates n and by the angular momentum J . A is the algebra E (3) of the Euclidean group in space. We find its irreducible representations by a novel approach, by showing that they are the irreducible representations (l (0), 0) of so(3, 1) , with l(0) or -l(0) being equal to the Casimir operator J (.) n . Any integer or half-integer l(0) is allowed. The Hilbert space of a particle of spin S ho sts 2S + 1 such representations. J can be analyzed into the sum L + S , i.e. pure spin states can be identified, provided 2S + 1 irreducible representations of A are glued together. These results apply to any surface which is diffeomorphic to S(2).- algebra: Weyl
- particle: spin
- operator: Casimir
- group: Euclidean
- sphere
- angular momentum
- algebra: E(3)
- algebra: Lie
- Clebsch-Gordan coefficients
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