Operator Algebras and Third Quantization

          @misc{ pirsa_PIRSA:25060015,
            doi = {10.48660/25060015},
            url = {https://pirsa.org/25060015},
            author = {Lashkari, Nima},
            keywords = {Quantum Gravity, Quantum Information},
            language = {en},
            title = {Operator Algebras and Third Quantization},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060015 see, \url{https://pirsa.org}}
          }
          

Abstract

In quantum gravity, the gravitational path integral involves a sum over topologies, representing the joining and splitting of multiple universes. To account for topology change, one is led to allow the creation and annihilation of both closed and open universes in a framework often called third quantization or universe field theory. We argue that since topology change in gravity is a rare event, its contribution to late-time physics should be universally governed by a Poisson distribution. In the Fock space of closed baby universes, this Poisson distribution corresponds to the statistics of the number operator in a coherent state, whereas allowing for the creation of asymptotic open universes calls for a non-commutative generalization of a Poisson process. We propose such an operator algebraic framework, called Poissonization, which takes as input the observable algebra and a (unnormalized) state of a quantum system and outputs a von Neumann algebra represented on its symmetric Fock space. Physically, our construction is a generalization of the coherent state vacua of bipartite quantum systems.