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• W3104081325 endingPage "145301" @default.
• W3104081325 startingPage "145301" @default.
• W3104081325 abstract "We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this task, non-standard (contact) symmetries are required as already shown in a previous article where the configuration-space quantization was given. The Hilbert space in the momentum space representation turns out to be made of a subset of (oscillatory) solutions of the Helmholtz equation in four dimensions. The most relevant result is the fact that both the scalar product and the generalized Fourier transform between configuration and momentum spaces deviate notably from the naively expected expressions, the former exhibiting now a non-trivial kernel, under a double integral, traced back to the non-trivial topology of the phase space, even though the momentum space as such is flat. In addition, momentum space itself appears directly as the carrier space of an irreducible representation of the symmetry group, and the Fourier transform as the unitary equivalence between two unitary irreducible representations." @default.
• W3104081325 created "2020-11-23" @default.
• W3104081325 creator A5051485761 @default.
• W3104081325 creator A5052387738 @default.
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• W3104081325 date "2020-03-19" @default.
• W3104081325 modified "2023-09-25" @default.
• W3104081325 title "$SU(2)$ -particle sigma model: momentum-space quantization of a particle on the sphere S 3" @default.
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• W3104081325 doi "https://doi.org/10.1088/1751-8121/ab661d" @default.
• W3104081325 hasPublicationYear "2020" @default.
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