36 citations · 148 across the 21 of their papers we have counts for
21 papers
Quantum Holonomies and the Heisenberg Group
J. E. Nelson, R. F. Picken
Quantum holonomies of closed paths on the torus are interpreted as elements of the Heisenberg group . Group composition in corresponds to path concatenation and th…
2+1 dimensional gravity
J. E. Nelson
It gives me great pleasure to review some of the joint work by Tullio Regge and myself. We worked intensely on 2+1-dimensional gravity from 1989 for about five years, and published…
Theory of intersecting loops on a torus
J. E. Nelson, R. F. Picken
We continue our investigation into intersections of closed paths on a torus, to further our understanding of the commutator algebra of Wilson loop observables in 2+1 quantum gravit…
Quantum geometry from 2+1 AdS quantum gravity on the torus
J. E. Nelson, R. F. Picken
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the…
A Quantum Goldman Bracket for Loops on Surfaces
J. E. Nelson, R. F. Picken
In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a --deformed representation of the fundamental group to derive signed area…
A quantum Goldman bracket in 2+1 quantum gravity
J. E. Nelson, R. F. Picken
In the context of quantum gravity for spacetimes of dimension 2+1, we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using p…