Topological methods in quantum gravity

Physics & Astronomy;quantum gravity;topological field theory

Starodubtsev, Artem

University of Waterloo

关键词: Physics & Astronomy;    quantum gravity;    topological field theory;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1217/1/astarodu2005.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The main technical problem with background independent approaches to quantum gravityis inapplicability of standard quantum field theory methods. New methods are needed whichwould be adapted to the basic principles of General Relativity. Topological field theoryis a model whichprovides natural tools for background independent quantum gravity.It is exactly soluble and, at the same time, diffeomorphism invariant. Applications oftopological field theory to quantum gravity include description of boundary statesof quantum General Relativity, formulation of quantum gravity as a constrained topological field theory,and a new perturbation theory which uses topological field theory as a starting point. The later is the central theme of the thesis. Unlike the traditional perturbation theoryit does not require splitting metric into a background and fluctuations, it is exactly diffeomorphisminvariant order by order, and the coupling constant of this theory is dimensionless.We describe the basic ideas and techniques of this perturbation theory as well as inclusion ofmatter particles, boundary states, and other necessary tools for studyingscattering problem in background independent quantum gravity.