There is No Band: Double Categories, Fragmented Spacetime, and an AQFT
David Lynch’s neo-noir classic Mulholland Drive challenges our sense of continuity, identity, and causality. In this talk, I use its fragmented narrative structure as a metaphorical guide to construct an algebraic quantum field theory using a double functor between free globularly generated double categories.
We define a double category of spacetime regions where vertical morphisms are inclusions, horizontal morphisms are causal maps, and squares ensure compatibility between the two. On the algebra side, we use Juan Orendain’s double category of von Neumann algebras and bimodules using a general construction from decorated bicategories. The result is a functor that captures how observables evolve and embed across spacetime in a way that traditional approaches don’t cleanly separate. We discuss how gluing and locality can be modelled in this construction.
Along the way, we use the storyline of Mulholland Drive to guide our intuition and structure the talk — from fragments of time and overlapping realities to a new way of understanding gluing and locality in field theory. No background in physics is assumed — just curiosity, and a willingness to follow a story where not everything is what it seems.