RT journal article
T1 SU(2)-particle sigma model: momentum-space quantization of a particle on the sphere S3
A1 Guerrero, Julio
A1 López Ruiz, Francisco Felipe
A1 Aldaya, Víctor
A2 Física Aplicada
K1 sigma model
K1 contact symmetries
K1 non-canonical quantization
K1 particle on the sphere
K1 momentum-space quantization
K1 non trivial topology
K1 Helmholtz equation
AB We perform the momentum-space quantization of a spin-less particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S3, 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 the 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.
PB IOP Publishing Ltd
SN 1751-8121
YR 2020
FD 2020-03-18
LK http://hdl.handle.net/10498/30442
UL http://hdl.handle.net/10498/30442
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026