Models of spontaneous wave function collapse. The GRW model (1986), the first model of wave function collapse, opened the way to a new approach to quantum mechanics, providing a coherent and unified description of all non-relativistic physical phenomena, both classical and quantum. Since then, many important successes have been achieved, and collapse models have proven to be compatible with all known physical phanomena. Research is very active at all levels: mathematical-physics (solutions and properties of the relevant equations), theoretical physics (relativistic models, connection of the collapse field with physical fields of Nature), phenomenology (non-quantum effects of spontaneous collapses), and experiments (new tests of the superposition principle of quantum mechanics).

Selected publications.

• GianCarlo Ghirardi, Alberto Rimini and Tullio Weber: “Unified dynamics for microscopic and macroscopic systems”, Physical Review D 34, 470 (1986).
• GianCarlo Ghirardi, Alberto Rimini and Philip Pearle: “Markov-processes in Hilbert-space and continuous spontaneous localization of systems of identical particles”, Physical Review A 42, 78 (1990).
• Angelo Bassi and GianCarlo Ghirardi: “Dynamical reduction models”, Physics Reports  379, 257 (2003).
• Stephen L. Adler and Angelo Bassi: "Is Quantum Theory Exact?", Science 325, 275 (2009).

Interface between classical and quantum mechanics. Classical (CM) and quantum (QM) mechanics are usually formulated using totally different tools, c-numbers for the first and operators in a Hilbert space for the second. Koopmann and von Neumann (KvN) in the 30's tried to bridge this gap by formulating also CM in a Hilbert space, albeit a different one than in QM. This bridge gets a more geometrical and physical meaning once it is formulated using path-integrals, which are the usual path-integral of Feynman for QM (which we will indicate with QPI) and a new one for the CM of KvN. This last path-integral has been called CPI to underlie its totally classical character. Using these tools some nice results have been obtained. For example the well-know Geometric Quantization method can be look at as a sort of dimensional reduction, and the non-superposition principle of CM seems to stem from some local universal invariances present in the CPI which disappears at the QPI level. To throw further light on the interplay between CM and QM, we are now exploring some new routes using the tools developed above. These new routes are based on techniques borrowed from the renormalization-group.

Selected publications.

• Ennio Gozzi, Martin Reuter, William D.Thacker: "Hidden BRS Invariance in Classical Mechanics II", Physical Review D 40 3363 (1989).
• Alexei A. Abrikosov (jr), Ennio Gozzi, Danilo Mauro: "Geometric Dequantization", Annals of Physics 317 24 (2005).
• Ennio Gozzi, Carlo Pagani: "Universal Local symmetries and non-superposition in classical mechanics", Physical Review Letters 105, 150604 (2010).