#### Date of Award

2008

#### Document Type

Honors Thesis (Open Access)

#### Department

Colby College. Physics and Astronomy Dept.

#### Advisor(s)

Robert T. Bluhm

#### Abstract

Einstein's general relativity is a geometrical theory of gravity in which the effects of gravity are due to the curvature of space and time. In contrast, all of the other fundamental particle interactions are described as quantum field theories that are invariant under gauge transformations. In efforts to unify gravity with these other particle theories, it is desirable to reexpress Einstein's general relativity as a gauge theory. The gauge symmetry in Einstein's theory can be identified as invariance under diffeomorphism transformations. This work examines the nature of this symmetry, how it is implemented, and how it behaves as a gauge transformation. Since spontaneous symmetry breaking and the Higgs mechanism are important in particle physics gauge theories, these same mechanisms will be examined as well for a gauge theory containing diffeomorphism symmetry. Using a fusion of well understood models from classical field theory and gauge theory, we investigate a gravity theory with a vector field that spontaneously breaks diffeomorphism symmetry. We conclude that spontaneous breaking, unlike conventional gauge theory, does not lead to the Higgs mechanism, and we examine the implications of this in greater detail.

#### Keywords

General relativity (Physics), Gauge fields (Physics)

#### Recommended Citation

Chung, John P., "Diffeomorphism invariance in general relativity" (2008).*Honors Theses.*Paper 53.

https://digitalcommons.colby.edu/honorstheses/53

#### Copyright

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