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====== Shah research blog, spring 2009 ====== This blog will record my progress in researching aspects of nonlinear flow (and applications of what we discuss in the study group) to quantum field theory. I am using Professor Gibson's blog as a template for how I construct this blog, so please let me know if there is anything I can do differently in formatting this blog. E-mail: <sarang.shah@gatech.edu> I will be updating this page over the next few days with a literature review of the problem and a brief introduction to quantum field theory. :-( 2009-1-27 Hello all, I have come down with a stomach virus and will be unable to make it to our install-fest. I will be installing channelflow on my copy of Linux and will post my progress on this blog today. I will also review my research into nonlinear field theories (in particular in n=m nonabelian Yang-Mills fields) and quantum chaos. :-( //Sorry to hear you're ill! Get well soon, and we'll see you next week. --John G.// :-) 2009-2-3 Installed Channelflow on my local linux installation. I will now work through the tutorial. Finished tutorial. I am still having a problem with installing the MATLAB scripts so that I can compile a movie. :-) Discussion of Chaos and Gauge Field Theory: :?: Is it possible to embed LaTeX directly into this wiki? The predominant means of understanding and developing the Standard Model interactions is through the use of Gauge Field Theory. In much the same way that we exact Lorentz invariance from our solutions in developing relativistic quantum theory, we demand that our fields also remain invariant under a gauge transformation, such as that of U(1), SU(2), and SU(3). Such a requirement entails the introduction of a gauge field in order for the action (Lagrangian) to remain stationary. It is from such consideration that the electromagnetic field A_μ is naturally introduced given an invariance of the action when ψ→exp(iθ)ψ. Yang-Mills Fields (http://en.wikipedia.org/wiki/Yang-Mills_field), result from an extension of ψ→exp(iθ)ψ, where ψ→exp(iθ^a T_a)ψ where a indexes the generators of a Lie Algebra. There is a Yang-Mills field A^a_μ for each generator. The nonabelian (noncommuting) nature of the generators T_a introduces further changes to the Field strength tensor. We may then assume that there is no energy flow and fix the gauge such that the Poynting vector vanishes A^a_0=0. The vacuum solution and conserved quantities lead to a partial differential equation in time and space for the field which may yield nonintegrable chaotic solutions.
