John Elias Roberts

Not to be confused with John A. G. Roberts? working in dynamical systems.

John Elias Roberts was 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, but his father came from the Llŷn Peninsula. He worked in Rome at Tor Vergata for a long time, before living his last few years in Goettingen.

John Roberts 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

- John Roberts,
*Mathematical Aspects of Local Cohomology*talk at Colloqium on Operator Algebras and their Applications to Mathematical Physics, Marseille 20-24 June, (1977)

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 ∞-categories. He conjectured that these are characterized by their ∞-nerves being complicial sets. This led Ross Street to develop the notion of orientals and formulate a precise version of this conjecture, which was proven by Dominic Verity. An account of this development is on pages 9-10 of

- Ross Street,
*An Australian conspectus of higher category theory*(pdf)

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.

On W*-categories:

- P. Ghez, Ricardo Lima, John E. Roberts,
*W*-categories*, Pacific Journal of Mathematics 120:1 (1985), 79–109, doi:10.2140/pjm.1985.120.79.

category: people

Last revised on April 24, 2021 at 17:45:48. See the history of this page for a list of all contributions to it.