Monday, July 2, 2012

1206.7060 (Maciej Trzetrzelewski)

Matrix regularization of embedded 4-manifolds    [PDF]

Maciej Trzetrzelewski
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 diffeomorphimsm 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).
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