Matrix regularization of embedded 4-manifolds
Mathematical Physics
2012-07-31 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S^3 also possible).
Cite
@article{arxiv.1206.7060,
title = {Matrix regularization of embedded 4-manifolds},
author = {Maciej Trzetrzelewski},
journal= {arXiv preprint arXiv:1206.7060},
year = {2012}
}
Comments
22 pages, v2: published version, minor corrections