A Hierarchical Finite Element Method for Quantum Field Theory
We study a model of scalar quantum field theory (QFT) in which spacetime is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get a renormalized action on the original triangle. The exact renormalization map between the angles of the triangles is obtained as well. The map can be used to find the partition function in scalar field theories in a recursive manner. A fixed point of this map is the cotangent formula in Finite Element Method which is used to find the energy stored in fields on a plane due to a Laplacian.