Topos theory and spacetime structure

According to the recently proposed model of spacetime, various difficulties of quantum field theories and semiclassical quantum gravity on curved 4-Minkowski spacetimes gain new formulations, leading to new solutions. The quantum mechanical effects appear naturally when diffeomorphisms are lifted to 2-morphisms between topoi. The functional measures can be well defined. Diffeomorphisms invariance and background independence are approached from the perspective of topoi. In the spacetimes modified at short distances by the internal structure of some topoi, the higher dimensional regions appear and field/strings duality emerges. We show that the model has natural extensions over extremely strong gravity sources in spacetime and shed light on the strong string coupling definition of B-type D-branes.

Topos theory
quantum gravity
field theory

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