ID 31751
file
title alternative
古典及び量子(2+1)次元重力の位相的側面
creator
Soda, Jiro
NDC
Physics
abstract
In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g = 0 and g = 1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g = 1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace naoclel of (2+1)-dimensional gravity with the matter fields in the case of g = 0 and y = 1. For g = 0, a wormhole solution is found but for g = 1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g = 1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity.
contents
ABSTRACT / p3
CONTENTS / p4
1 Introduction / p5
2 ADM Canonical Formalism / p9
3 York's Formalism / p13
4 Evolution of the Geometry / p17
5 Phase Space Reduction / p23
6 Linearized Gravity / p27
7 Mini-superspace / p31
8 Quantum Gravity / p35
9 Conclusion / p44
Appendix A / p46
Appendix B / p48
Appendix C / p54
SelfDOI
language
eng
nii type
Thesis or Dissertation
HU type
Doctoral Theses
DCMI type
text
format
application/pdf
text version
ETD
rights
Copyright(c) by Author
relation references
・A. Hosoya and J. Soda, Mod. Phys. Lett. A4 (1989) 2539,
・J. Soda, to be published in Prog. Theor. Phys. Vol.83 No.4 (April),
・Y. Fujiwara and J. Soda, to be published in Frog. Theor. Phys. Vol.83 No.4 (April).
relation references URL
http://dx.doi.org/10.1142/S0217732389002847
http://dx.doi.org/10.1143/PTP.83.805
http://dx.doi.org/10.1143/PTP.83.733
grantid
甲第831号
degreeGrantor
広島大学(Hiroshima University)
degreename Ja
博士(理学)
degreename En
Physical Science
degreelevel
doctoral
date of granted
1990-03-26
department
Graduate School of Science