Quantum Finite Elements: The Affine Projection for Lattice Field Theory on Curved Manifolds

Explore an advanced lecture on extending lattice field theory to curved spaces using Quantum Finite Elements (QFE). Delve into the complexities of adapting traditional methods to smooth Riemann manifolds, focusing on the development of QFE compatible with discrete quantum geometry on simplicial complexes. Examine the treatment of ultraviolet perturbative counter terms and the affine projection between flat and curved spaces. Analyze practical applications through tests on 2D and 3D Ising conformal field theory (CFT) on spheres and cylinders. Gain insights into potential generalizations of Affine QFE and its extensions to theories involving fermionic and gauge fields. This in-depth presentation by Richard Brower, delivered on November 24, 2022, at the Dublin Institute for Advanced Studies (DIAS), offers nearly two hours of cutting-edge theoretical physics exploration.