SU(2) particle sigma model: The role of contact symmetries in global quantization

DOI: 
10.1088/1751-8113/49/50/505201
Publication date: 
01/12/2016
Main author: 
Aldaya V.
IAA authors: 
Aldaya, V.;Guerrero, J.;Cossío, F.
Authors: 
Aldaya V., Guerrero J., López-Ruiz F.F., Cossío F.
Journal: 
Journal of Physics A: Mathematical and Theoretical
Refereed: 
Yes
Publication type: 
Article
Volume: 
49
Pages: 
Number: 
505201
Abstract: 
In this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S 3, by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-invariant at the classical level, although not necessarily the Lagrangian. Special attention is paid to the role played by the basic quantum commutators, which depart from the canonical, Heisenberg-Weyl ones, as well as the relationship between the integration measure in the Hilbert space of the system and the non-trivial topology of the configuration space. Also, the quantization on momentum space is briefly outlined. © 2016 IOP Publishing Ltd.
Database: 
SCOPUS
ADS
URL: 
https://ui.adsabs.harvard.edu/#abs/2016JPhA...49.5201A/abstract
ADS Bibcode: 
2016JPhA...49.5201A
Keywords: 
contact symmetries; non trivial topology; non-canonical quantization; nonlinear systems; particle sigma model