Recursive and Exact New Quantum Theory (ReNewQuantum)

ERC Synergy Grant 810573/2019

The overarching goal of ReNewQuantum is to renew the mathematical foundation behind quantum phenomena.
We aim to construct a recursive and exact new approach to quantum theory. Quantum theory is one of the pillars of modern science. Its success stretches from elementary quantum mechanical models, developed a century ago by quantization of classical mechanics, to advanced quantum field theories such as the standard model of particle hysics, which is the quantization of a gauge theory. However, a precise and universal mathematical formulation of the quantization procedure is still lacking. In addition, there are very few analytic methods in Quantum Mechanics and in Quantum Field Theory. They are typically based on approximation schemes which often lead to quantitative and even qualitative failures in our descriptions.

In response to these shortcomings, the main objective of ReNewQuantum is to construct a completely new mathematical approach to quantization and to quantum systems. This quantum theory will provide:
- a global, explicit and recursive description of the series of quantum corrections,
- access to exact quantum regimes beyond perturbation theory,
- a well founded mathematical theory underlying the quantization procedure, based on geometric structures, and applicable to quantum field theory and string theory.

ReNewQuantum will take the lead among the world scientific community in building this new theory of quantum physics. The researchers behind ReNewQuantum have already made important contributions along these directions. The construction of a recursive and exact new approach to quantum theory with the stated properties will only be possible through their joint synergetic effort and a combination of their deep mathematical and physical expertises, including geometry, topology and the mathematical theory of quantization (Andersen, Kontsevich), and quantum mechanics, quantum field theory, random matrix theory and string theory (Eynard, Mariño).