Title: Quantum Finite Elements: The Affine projection for Lattice field theory on Curved Manifolds

Abstract: Extending traditional lattice field theory beyond flat space to a smooth Riemann manifolds requires a Quantum extension of Finite Elements (QFE) compatible with the discrete quantum geometry of a “triangulated” simplicial complex. Consideration of ultraviolet perturbative counter terms, the affine projection between flat and curved space are developed and tested in the context of the 2d and 3d Ising conformal field theory (CFT) on spheres and cylinders. Speculations on a more general approach Affine QFE and extensions  to theories with fermionic  and gauge fields will be hazarded.

Talk – Video

Talk – Slides