What is quantization? Jeffrey, Karshon, and Weitsman have excelled in answering this question for Hamiltonian systems, particularly in the context of group actions. I will apply their insights to quantize classical systems on manifolds with boundary, explaining joint work with Jonathan Weitsman.

I will then transition to Topological Quantum Field Theory (TQFT) and explore how to quantize Turing-complete dynamical systems, including those associated with Fluid Dynamics (joint work with Ángel Gonzalez-Prieto and Daniel Peralta-Salas). This exploration will lead us to an abstract design of a computational field theory (which we call the Hybrid Computer) as a Topological Field Theory, which we term TKFT in honor of Stephen Kleene's work on partial recursive functions. This hybrid computer computes and "quantizes" physical systems. TKFTs are built up from basic pieces, including "flubits." A flubit is associated with a 3D Turing-complete Euler flow.