Giuseppe MARMO
The Groupoidal Approach to Quantum Mechanics and Information Geometry
Recently, in a series of papers with several collaborators, we have shown that Schwinger's approach to quantum mechanics is properly described by means of groupoids and 2-groupoids.
Lie groupoids provide also the proper framework to deal with statistical manifolds by means of potential functions ( relative entropies)both at the classical and quantum level.I will try to explain why groupoids provide the appropriate setting to deal with theories which possess a statistical-probabilistic description.
