A Hierarchical Finite Element Method for Quantum Field Theory
Mathematical Physics
2013-09-18 v2 High Energy Physics - Lattice
High Energy Physics - Theory
math.MP
Abstract
We study a model of scalar quantum field theory in which space-time 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. A fixed point of this map happens to be the cotangent formula of Finite Element Method which approximates the Laplacian in two dimensions.
Cite
@article{arxiv.1305.3322,
title = {A Hierarchical Finite Element Method for Quantum Field Theory},
author = {Arnab Kar and Fred Moolekamp and S. G. Rajeev},
journal= {arXiv preprint arXiv:1305.3322},
year = {2013}
}