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Author ORCID Identifier

https://orcid.org/0000-0001-8623-0293

AccessType

Open Access Dissertation

Document Type

dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2022

Month Degree Awarded

May

First Advisor

Owen Gwilliam

Subject Categories

Algebra | Elementary Particles and Fields and String Theory | Geometry and Topology | Other Mathematics

Abstract

In this thesis we develop a formulation of general covariance, an essential property for many field theories on curved spacetimes, using the language of stacks and the Batalin-Vilkovisky formalism. We survey the theory of stacks, both from a global and formal perspective, and consider the key example in our work: the moduli stack of metrics modulo diffeomorphism. This is then coupled to the Batalin-Vilkovisky formalism–a formulation of field theory motivated by developments in derived geometry–to describe the associated equivariant observables of a theory and to recover and generalize results regarding current conservation.

DOI

https://doi.org/10.7275/28580579

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Available for download on Sunday, November 13, 2022

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