Edward Nelson said "First quantization is a mystery\, but second quantization is a functor". This functor takes the Hilbert space H representing a quantum mechanical system\, and gives i ts Fock space F(H)\, representing a multi-particle system with any number of indistinguishable copies of the original system as in quantum field the ory (I am considering the bosonic case). In a categorical analysis of the harmonic oscillator\, Vicary revised Nelson's slogan to say "second quanti zation is a monad" - that is\, the functor in question is equipped with so me extra algebraic structure\, making it the "Fock Monad" (F\,$\\eta$\,$\\ epsilon$).
\n\nGroupoidification is one of a number of approaches to "categorifying" quantum-mechanical systems: finding higher-categorical an alogs of those systems. It uses a 2-category Span(Gpd) whose objects are g roupoids\, and whose morphisms are "spans". This has had some success in d escribing extensions of topological field theory to systems with boundary\ , with the "categorified" theory describing the evolution of open systems\ , which can be composed along their boundaries\, over time. In this talk\, I will use this framework to describe a categorification of F to the "Foc k Pseudomonad" which can be defined in any suitable 2-category\, and the c ompatibility of this pseudomonad in Span(Gpd) with that in 2-Hilbert space s\, and\, under the "degroupoidification" map\, with the usual Fock constr uction on Hilbert spaces.
\n LOCATION:https://researchseminars.org/talk/TQFT/49/ END:VEVENT END:VCALENDAR