descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 07 Oct 2019Embargo end date: 01 Jan 2018 English Publisher:World Scientific Pub Co Pte LtdJournal:Modern Physics Letters A, volume 34, page 1,950,256 (issn: 0217-7323, eissn: 1793-6632,

Authors: J. E. Nelson; R. F. Picken;

doi: 10.1142/s0217732319502560 , 10.48550/arxiv.1808.08812

arXiv: http://arxiv.org/abs/1808.08812

handle: 2318/1694399

Quantum holonomies and the Heisenberg group

- Summary
- Subjects
- Metrics

Abstract

Quantum holonomies of closed paths on the torus [Formula: see text] are interpreted as elements of the Heisenberg group [Formula: see text]. Group composition in [Formula: see text] corresponds to path concatenation and the group commutator is a deformation of the relator of the fundamental group [Formula: see text] of [Formula: see text], making explicit the signed area phases between quantum holonomies of homotopic paths. Inner automorphisms of [Formula: see text] adjust these signed areas, and the discrete symplectic transformations of [Formula: see text] generate the modular group of [Formula: see text].

Related Organizations

Keywords

High Energy Physics - Theory, Quantum Physics, High Energy Physics - Theory (hep-th), FOS: Physical sciences, 81R50 - 83C45, group: Heisenberg | group: modular | transformation: symplectic | holonomy | commutation relations | deformation | torus, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Mathematical Physics

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average