Gwilliam, OwenDul, Filip2024-04-262024-04-262022-052022-0510.7275/28589712https://hdl.handle.net/20.500.14394/18853In 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.Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/general covariancestackshomological algebraclassical field theorycurved spacetimeAlgebraElementary Particles and Fields and String TheoryGeometry and TopologyOther MathematicsDissertation (Open Access)https://orcid.org/0000-0001-8623-0293