Quantum localisation on the circle

Autor(es)

Fresneda, Rodrigo ^[1] ; Gazeau, Jean Pierre ^{[2, 3]} ; Noguera, Diego ^[2]

Afiliação do(s) autor(es)

^[1] Fed Univ ABC UFABC, BR-09210580 Santo Andre, SP - Brazil

^[2] Ctr Brasileiro Pesquisas Fis, Rua Xavier Sigaud 150, BR-22290180 Rio De Janeiro, RJ - Brazil

^[3] Univ Paris Diderot, APC, UMR 7164, Sorbonne Paris Cite, F-75205 Paris - France

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 59, n. 5 MAY 2018.
• Citações Web of Science: 2

Resumo

Covariant integral quantisation using coherent states for semi-direct product groups is implemented for the motion of a particle on the circle. In this case, the phase space is the cylinder, which is viewed as a left coset of the Euclidean group E(2). Coherent states issued from fiducial vectors are labeled by points in the cylinder and depend also on extra parameters. We carry out the corresponding quantisations of the basic classical observables, particularly the angular momentum and the 2 pi-periodic discontinuous angle function. We compute their corresponding lower symbols. The quantum localisation on the circle is examined through the properties of the angle operator yielded by our procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. Comparison with other approaches to the long-standing question of the quantum angle is discussed. Published by AIP Publishing. (AU)

• Processo FAPESP: 16/03319-6 - Métodos não perturbativos em teoria quântica e em TQC e aplicações deles aos problemas de física atuais
• Beneficiário: Dmitri Maximovitch Guitman
• Modalidade de apoio: Auxílio à Pesquisa - Temático