Document Type


Date of Degree

Spring 2018

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Rodgers, Vincent G.

First Committee Member

Meurice, Yannick

Second Committee Member

Polyzou, Wayne Nicholas

Third Committee Member

Fang, Hao

Fourth Committee Member

Onel, Yasar


The diffeomorphism field is introduced to the physics literature in [1] where it arises as a background field coupled to Polyakov’s quantum gravity in two dimensions, where Einstein’s gravity is trivial. Moreover, it is seen in many ways as the gravitational analog of the Yang-Mills field. This raises the question of whether the diffeomorphism field exists in higher dimensions, playing an essential role in gravity either by supplementing Einstein’s theory or by modifying it.

With this motivation, several distinct theories governing the dynamics of the diffeomorphism field have been constructed and developed by mimicking the construction of the Yang-Mills theory from the Kac-Moody algebra. This analogy, however, is not perfect and there are many subtleties and difficulties encountered.

This thesis constitutes a further development. The previously proposed theories are carefully examined; certain subtleties and problems in them have been discovered and made apparent. Some of these problems have been solved, and for others possible routes to follow have been laid down. Finally, other geometric approaches than the ones followed before are investigated.


diffeomorphism field, quantum gravity, Virasoro algebra


x, 206 pages


Includes bibliographical references (pages 202-206).


Copyright © 2018 Delalcan Kilic

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