Meusburger C (2006)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2006
Publisher: Springer Verlag (Germany)
Book Volume: 266
Pages Range: 735-775
Journal Issue: 3
DOI: 10.1007/s00220-006-0037-x
We relate the geometrical construction of (2+1)-spacetimes via grafting to phase space and Poisson structure in the Chern-Simons formulation of (2+1)-dimensional gravity with vanishing cosmological constant on manifolds of topology ℝ times S , where S is an orientable two-surface of genus g>1. We show how grafting along simple closed geodesics λ is implemented in the Chern-Simons formalism and derive explicit expressions for its action on the holonomies of general closed curves on S .We prove that this action is generated via the Poisson bracket by a gauge invariant observable associated to the holonomy of λ. We deduce a symmetry relation between the Poisson brackets of observables associated to the Lorentz and translational components of the holonomies of general closed curves on S and discuss its physical interpretation. Finally, we relate the action of grafting on the phase space to the action of Dehn twists and show that grafting can be viewed as a Dehn twist with a formal parameter θ satisfying θ = 0.
APA:
Meusburger, C. (2006). Grafting and poisson structure in (2+1)-gravity with vanishing cosmological constant. Communications in Mathematical Physics, 266(3), 735-775. https://doi.org/10.1007/s00220-006-0037-x
MLA:
Meusburger, Cathérine. "Grafting and poisson structure in (2+1)-gravity with vanishing cosmological constant." Communications in Mathematical Physics 266.3 (2006): 735-775.
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