Geometry and Symmetry in Quantum Field Theory




This project is a continuation of the previous Iniziativa Specifica with the same title, and it’s aimed at moving forward on the basis of improved motivations.  Highly formalized aspects of (classical and) quantum field theories are the core of the research interests of the participants. Afterwards, rather than focusing sharply on a few topics, we keep on looking for ‘windows’ into, and across, a variety of problems that share similar mathematical methods. 

Referring to quantum gravity as one of the common threads of the project, we intend to explore the multi-faceted landscape of current approaches, ranging from string theory, quantum field theory on curved spacetimes and canonical quantization up to non-commutative deformations and generalized (twisted, q-deformed, …) symmetries.  In particular, low-dimensional and analogue models, as well as approximations and discretizations, have represented an effective and critical test-bed in the search and in the analysis of  consistent  quantization schemes  for gravity, and we intend to further exploit potential synergies and interconnections.

Over the years our collaboration has produced a large literature of results addressing many of these topics. The complex scenario of techniques adopted, and often improved in a significant way, has  stimulated a growth in expertise and in the understanding of the conceptual issues behind QFTs and their symmetries, suggesting further connections also in view of applications to  many-body quantum  systems, condensed matter physics, complex networks and quantum information theory.




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