Abstract
We study some aspects of gauge invariant observables in Witten's new approach to canonical 2+1 dimensional gravity as a Chern-Simons gauge theory. We derive the Poisson brackets of the Wilson line observables in the case that space is topologically the plane with N isolated points removed. The infinitely many Wilson line observables provide a complete but highly redundant description of the physical phase space. We eliminate this redundancy by showing how to write any Wilson line as a function of a finite set of observables. The Poisson brackets of this finite set of observables from a non-trivial closed algebra which has an interesting structure. We solve the quantum operator ordering problem and thus convert the classical Poisson bracket algebra into a quantum mechanical commutator algebra. We argue that this algebra could serve as an alternative starting point for 2+1 dimensional gravity.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call