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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/10.7275/28589712
Recommended Citation
Dul, Filip, "GENERAL COVARIANCE WITH STACKS AND THE BATALIN-VILKOVISKY FORMALISM" (2022). Doctoral Dissertations. 2515.
https://doi.org/10.7275/28589712
https://scholarworks.umass.edu/dissertations_2/2515
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Included in
Algebra Commons, Elementary Particles and Fields and String Theory Commons, Geometry and Topology Commons, Other Mathematics Commons