Mathematical Physics has a twofold scope: that of solving mathematical problems arising from physical theories and also that of finding and developing mathematical structures that can be useful in physics, on the basis of mathematical intuition and beauty of its language. Past and recent history of physics teaches us that sometime mathematical beauty comes before physical use and this must not be forgotten. Within this framework, the research lines in Mathematical Physics of our department are the following.
- Quantum tomography: reconstructing an unknown state of a quantum system from the knowledge of the probability distribution of certain physical quantities.
- Supersymmetry: study of supergroups and their representations.
- Conceptual problems at the foundations of quantum mechanics.
- Foundations of statistical mechanics: extension to the quantum case of Boltzmann’s analysis concerning the convergence to thermodynamic equilibrium of macroscopic systems initially in a non-equilibrium state.
- Nanostructures and quantum computation.
- Algebraic structures and their possible use in physical theories beyond the standard model of elementary particle physics.