Folkert Kuipers (INFN Napoli)

Stochastic Mechanics, Second Order Geometry and the Quantum Foam

The search for a theory that consistently combines quantum theory with general relativity forces us to consider geometrical frameworks beyond standard (first order) differential geometry. One candidate for such a generalized geometrical framework is second order geometry, which was invented to deal with the apparent breaking of general covariance, due to the violation of Leibniz’ rule in stochastic theories. 

In this talk, I will extensively motivate the use of stochastic differential geometry in the study of quantum gravity by reviewing the tight connections between quantum theories and stochastic theories. Then, I will review the basic ingredients of second order geometry and show how it can be employed to study both Euclidean and Lorentzian quantum theories in curved spacetimes. Finally, if time permits, I will discuss some new results on the relations between spacetime stochasticity and spacetime non-commutativity.