Lattice instantons in the large dimension limit |
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Authors: | Bernard Grossman Thomas W Kephart |
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Institution: | (1) Department of Physics, Rockefeller University, 10021 New York, NY, U.S.A.;(2) Department of Physics and Astronomy, Vanderbilt University, 37235 Nashville, TN, U.S.A. |
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Abstract: | We give a lattice construction of the discretizations of the topologically nontrivial maps S
2n–1 S
n
. For n=1, 2, 4, 8, these are the Hopf maps. The construction, based on Barnes-Wall lattices, Reed-Muller error-correcting codes, and Hadamard matrices, generalizes to n=2
i
for i any integer. Manton's result for the cases n=2 and 4 (i.e., the monopole and instanton) are included. We argue that discrete harmonic analysis will be exact in the infinite dimension limit.Work supported in part by the DOE contract #DE-ACO2-87ER-40325.B.Department of Energy Outstanding Junior Investigator supported in part by DOE contract number DE-FGO5-85ER-40226. |
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Keywords: | 81E15 82A68 |
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