arXiv subjects

C Meusburger

Publications and source records attributed to C Meusburger.

3 recordsLinked to original sources

arXiv2005

Phase space structure of Chern-Simons theory with a non-standard puncture

We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G\ltimes g^*$ on a three-manifold of topology $R \times S$, where $S$ is a surface of genus $g$ with $n+1$ punctures. At each puncture additional variables are introduced and coupled minimally to the Chern-Simons gauge field. The first $n$ punctures are treated in the usual way and the additional variables lie on coadjoint orbits of $G\ltimes g^*$. The $(n+1)$st puncture plays a distinguished role and the associated variables lie in the cotangent bundle of $G\ltimes g^*$. This allows us to impose a curvature singularity for the Chern-Simons gauge field at the distinguished puncture with an arbitrary Lie algebra valued coefficient. The treatment of the distinguished puncture is motivated by the desire to construct a simple model for an open universe in the Chern-Simons formulation of $(2+1)$-dimensional gravity.

hep-th↗

arXiv2005

Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent bundle of the Poincaré group, and coupled minimally to the Chern-Simons gauge field. We apply this description of spatial infinity to open universes of general genus and with an arbitrary number of massive spinning particles. Using results of [9] we give a finite dimensional description of the phase space and determine its symplectic structure. In the special case of a genus zero universe with spinless particles, we compare our result to the symplectic structure computed by Matschull in the metric formulation of (2+1)-dimensional gravity. We comment on the quantisation of the phase space and derive a quantisation condition for the total mass and spin of an open universe.

gr-qc↗

arXiv2004

The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G\ltimes \mathfrak{g}^*$

We quantise a Poisson structure on H^{n+2g}, where H is a semidirect product group of the form $G\ltimes\mathfrak{g}^*$. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ on $R \times S_{g,n}$, where S_{g,n} is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$. We construct the quantum algebra and its irreducible representations and show that the quantum double D(G) of the group G arises naturally as a symmetry of the quantum algebra.

hep-th↗