Quantum differential geometric methods in theoretical physics

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Quantum differential geometry was developed in recent years as an extension to geometry to allow the "coordinate algebra" of a space to be noncommutative and/or for differential forms to not commute with coordinates.Our current project consists of applying these mathematical concepts to theoretical and mathematical physics in order to have a description of physics when the underlying spacetime is noncommutative. Specifically, we are adapting the main constructions of classical field theory, such as the jet bundle and the variational bicomplex, to noncommutative spacetimes. This would then allow for the first time a systematic formulation of the Euler-Lagrange equations and Noether theorems for noncommutative spacetimes.