Quantum holonomies of closed paths on the torus $IT^2$ are interpreted as elements of the Heisenberg group $H_1$. Group composition in $H_1$ corresponds to path concatenation and the group commutator is a deformation of the relator of the fundamental group $pi_1$ of $IT^2$, making explicit the signed area phases between quantum holonomies of homotopic paths. Inner automorphisms of $H_1$ adjust these signed areas, and the discrete symplectic transformations of $H_1$ generate the modular group of $IT^2$.

QUANTUM HOLONOMIES AND THE HEISENBERG GROUP

J. E. Nelson;
2019-01-01

Abstract

Quantum holonomies of closed paths on the torus $IT^2$ are interpreted as elements of the Heisenberg group $H_1$. Group composition in $H_1$ corresponds to path concatenation and the group commutator is a deformation of the relator of the fundamental group $pi_1$ of $IT^2$, making explicit the signed area phases between quantum holonomies of homotopic paths. Inner automorphisms of $H_1$ adjust these signed areas, and the discrete symplectic transformations of $H_1$ generate the modular group of $IT^2$.
2019
34
31
1
1
https://www.worldscientific.com/action/doSearch?ContribAuthorStored=Nelson,+J+E
group: Heisenberg | group: modular | transformation: symplectic | holonomy | commutation relations | deformation | torus
J.E.Nelson;R.F.Picken
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1694399
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