John Roberts is a mathematical physicist who works on the mathematical foundations of quantum mechanics and quantum field theory in terms of AQFT.
John Roberts was born in England, his father came from the Llŷn Peninsula. He has worked in Rome at Tor Vergata for a long time.
John Robers wrote his PhD thesis was on rigged Hilbert spaces, a way of making Dirac’s description of quantum mechanics precise. After that he followed the Haag-Kastler approach for axiomatizing quantum theory and became one of its central proponents.
Early on he suggested in
that local nets of observables should carry a notion of cohomology – or rather of nonabelian cohomology – with coefficients in an ∞-category. Motivated by this he was one of the first to consider strict ω-categories. He conjectured that these are characterized by their ω-nerves being complicial sets. This led Ross Street to develop the notion of orientals and eventually to prove this conjecture. An account of this development is on pages 9-10 of
Later Roberts proved together with Doplicher what is now one of the central results in AQFT, the Doplicher-Roberts reconstruction theorem – a version of Tannaka duality – which in the context of AQFT serves to intrinsically characterize the superselection sectors of a QFT. See also DHR superselection theory.