Quantum geometry from 2+1 AdS quantum gravity on the torus

被引：3

作者：

Nelson, J. E. ^{[1
,2
]}

Picken, R. F. ^{[3
,4
]}

机构：

[1] Univ Turin, Dipartimento Fis Teor, I-10125 Turin, Italy

[2] INFN, Sez Torino, I-10125 Turin, Italy

[3] Univ Tecn Lisbon, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

[4] Univ Tecn Lisbon, Inst Super Tecn, CAMGSD, P-1049001 Lisbon, Portugal

来源：

GENERAL RELATIVITY AND GRAVITATION | 2011年 / 43卷 / 03期

关键词：

Wilson observables; 2+1 Quantum gravity; Goldman bracket; Area phases; (2+1)-DIMENSIONAL GRAVITY; QUANTIZATIONS; CONNECTIONS; HOLONOMIES; DIMENSIONS; LOOPS;

D O I：

10.1007/s10714-010-1095-0

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

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 observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.

引用

页码：777 / 795

页数：19

共 20 条

[1]

[Anonymous], 1994, NONCOMMUTATIVE GEOME

[2] COMPARATIVE QUANTIZATIONS OF (2+1)-DIMENSIONAL GRAVITY [J].