Quantum holonomies and the Heisenberg group-Reference-Cited by-同舟云学术

Quantum holonomies and the Heisenberg group

Published:2019-10-07 Issue:31 Volume:34 Page:1950256
ISSN:0217-7323
Container-title:Modern Physics Letters A
language:en
Short-container-title:Mod. Phys. Lett. A

Author:

Nelson J. E.¹^ORCID,Picken R. F.²

Affiliation:

1. Dipartimento di Fisica Sezione Teorica, Università degli Studi di Torino and INFN Sezione di Torino, via Pietro Giuria 1, Torino 10125, Italy

2. Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, Lisboa 1049-001, Portugal

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].

Funder

INFN

FCT

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217732319502560

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