Monday, February 4, 2013
How to decode relativistic PDE
In several papers, including one under submission, I have proposed new PDE systems to study,
which would try to answer, for example, the question "what is an electron?" One of the PDE systems in the new paper is the most credible well-specified option I know of as yet to model the universe.
Mathematicians who know about PDE have a huge amount to contribute, to enrich our understanding of this family of models. Even the more familiar BPS model of physics could benefit from some more formal, rigorous analysis -- and the new models are more complicated, as is necessary to fit with empirical reality, and to get closer to the standard model of physics.
However -- knowing a lot about PDE mathematics and dynamical systems does not always make it easy to confidently decode classic papers like those of 'tHooft and Prasad and Sommerfield, let alone the new Lagrangians and the standard model of physics. Thus yesterday I wrote up a kind of
"cheat sheet," a very brief condensed paper, for the benefit of mathematicians interesting in decoding
this literature (including relativistic Lagrangian field theory in general):