Discrete spacetime volume for three-dimensional BF theory and quantum gravity

被引：31

作者：

Freidel, L ^{[1
]}

Krasnov, K

机构：

[1] Penn State Univ, Dept Phys, Ctr Gravitat Phys & Geometry, University Pk, PA 16802 USA

[2] Ecole Normale Super Lyon, Phys Theor Lab, ENSLAPP, F-69364 Lyon 07, France

来源：

CLASSICAL AND QUANTUM GRAVITY | 1999年 / 16卷 / 02期

关键词：

D O I：

10.1088/0264-9381/16/2/003

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

The Turaev-Viro state sum invariant is known to give the transition amplitude for the three-dimensional BF theory with cosmological term, and its deformation parameter (h) over bar is related to the cosmological constant via (h) over bar = root Lambda. This suggests a way to find the expectation value of the spacetime volume by differentiating the Turaev-Viro amplitude with respect to the cosmological constant. Using this idea, we find an explicit expression For the spacetime volume in BF theory. According to our results, each labelled triangulation carries a volume that depends on the labelling spins. This volume is explicitly discrete. We also discuss the possibility of using the Turaev-Viro model to obtain the spacetime volume for (2 + 1)-dimensional quantum gravity.

引用

页码：351 / 362

页数：12

共 17 条

[1] Quantum theory of geometry: I. Area operators [J].

Ashtekar, A ;

Lewandowski, J .

CLASSICAL AND QUANTUM GRAVITY, 1997, 14 (1A) :A55-A81

[2]

Ashtekar A., 1998, Adv. Theor. Math. Phys, V1, P388, DOI DOI 10.4310/ATMP.1997.V1.N2.A8

[3]

BAEZ JC, 1996, INTERFACE KNOTS PHYS, P167

[4] ON THE VASSILIEV KNOT INVARIANTS [J].

BARNATAN, D .

TOPOLOGY, 1995, 34 (02) :423-472

[5]

CARLIP S, 1995, LECT 2 PLUS 1 DIMENS

[6]

DAUGHTON A, 1998, GRQC9805101

[7]

FREIDEL L, 1999, UNPUB

[8]

FRIEDEL L, 1998, HEPTH9807092

[9]

Hawking SW., 2010, General Relativity: An Einstein Centenary Survey

[10] Spectrum of the volume operator in quantum gravity [J].

Loll, R .

NUCLEAR PHYSICS B, 1996, 460 (01) :143-154

← 1 2 →