Fast Blow Up in the (4+1)-dimensional Yang Mills Model and the(2+1)-dimensional S² Sigma Model

1999/09/13 by Jean Marie Linhart, Linhart, Jean Marie
Mathematics · Physics and Astronomy · #35L15 (Primary) 25-04 #35L70 #35Q51 #35Q60 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:25-04 #msc:35L15 #msc:35L70 #msc:35Q51 #msc:35Q60

paper · pdf · doi:10.48550/arxiv.math-ph/9909015

32 pages, 9 figures

arxiv created 1999/09/13 · arxiv updated 2009/11/30

Abstract

We study singularity formation in spherically symmetric solitons of the (4+1) dimensional Yang Mills model and the charge two sector of the (2+1) dimensional S² sigma model, also known as \IC P¹ wave maps, in the adiabatic limit. These two models are very similar. Studies are performed numerically on radially symmetric solutions using an iterative finite differencing scheme. Predictions for the evolution toward a singularity are made from an effective Lagrangian and confirmed numerically. In both models a characterization of the shape of a time slice f(r,T) with T fixed is provided, and ultimately yields an new approximate solutions to the differential equations that becomes exact in the adiabatic limit.

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