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 epsilon(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 hosts 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).
On the Weyl algebra for a particle on a sphere
BRACCI, LUCIANO;PICASSO, LUIGI ETTORE
2011-01-01
Abstract
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 epsilon(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 hosts 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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
