My research interest is in solving Hilbert's sixth problem about physics axiomatization. Recently I obtained an axiomatization of quantum mechanics in the C*-algebraic formalism based on the existence of time, a configuration space defined as a manifold with a tensor product with unit, local invariance of the laws of nature under non-stochastic time evolution, invariance of the laws of nature under composability and translations in phase space, non-existence of negative mass, non-contextuality of truth, and violations of Bell inequalities. I also uncovered a new mathematical structure (a tensor product group) which explains the collapse postulate while preserving unitarity.
Quantum mechanics axiomatization generalizes naturally into non-commutative geometry using non-division number systems when one removes the constraint of strict norm positivity, and the Standard Model is best expressed as a spectral triple in Connes' non-commutative geometry framework.
The quantum mechanics axiomatization which recovers the usual C*-algebraic formalism implies a new quantum mechanics interpretation which restores realism in a new way.
As a key postulate of the axiomatization, the necessity of time can be recovered by pure non-commutativity effects on von Neumann algebras, but this also needs an explanation outside quantum mechanics as well. Studying the emergence of causality by the non-contextuality of truth in nature is another research direction. In predicate logic, non-contextuality leads the fact that all universally true statements are provable which leads to causality. The goal is to generalize this proof to all logical systems if possible, and if not, understanding the limitations of such a result.
