The Torus Universe in the Polygon Approach to 2 + 1 - Dimensional

نویسنده

  • M. Welling
چکیده

In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we nd that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we describe the matter-free toroidal spacetime in ’t Hooft’s polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes....

متن کامل

Quantization of 2+1 Gravity on the Torus

We use the polygon representation of 2+1–dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-classinvariant wave function for a quantum ”big bounce”, is reminiscent of the interference patterns of linear gratings. We consider the “problem of time” of quantum gravity: for one choice of internal time the universe recovers ...

متن کامل

Transition Amplitude in 2+1 dimensional Chern-Simons Gravity on a Torus

In the framework of the Chern-Simons gravity proposed by Witten, a transition amplitude of a torus universe in 2+1 dimensional quantum gravity is computed. This amplitude has the desired properties as a probability amplitude of the quantum mechanics of a torus universe, namely, it has a peak on the ”classical orbit” and it satisfies the Shrödinger equation of the 2+1 dimentional gravity. The di...

متن کامل

ar X iv : h ep - t h / 04 08 08 8 v 1 1 1 A ug 2 00 4 Milne and Torus Universes Meet

Three dimensional quantum gravity with torus universe, T 2 ×R, topol-ogy is reformulated as the motion of a relativistic point particle moving in an Sl(2, Z) orbifold of flat Minkowski spacetime. The latter is precisely the three dimensional Milne Universe studied recently by Russo as a background for Strings. We comment briefly on the dynamics and quantization of the model. Stanley has made ma...

متن کامل

Spacetime Singularities in (2+1)-Dimensional Quantum Gravity

The effects of spacetime quantization on black hole and big bang/big crunch singularities can be studied using new tools from (2+1)dimensional quantum gravity. I investigate effects of spacetime quantization on singularities of the (2+1)-dimensional BTZ black hole and the (2+1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a “quantum generalized affine paramete...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007