Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Questions about *classical* gauge field theory (Abelian and Non-Abelian)

  1. Sep 5, 2010 #1
    I know little about these issues, so my questions may be dumb.
    1. Do exact solutions exist for non-Abelian gauge theory without matter fields?
    2. Do exact solutions exist for Abelian/Non-Abelian theory with matter fields (scalar or spinor)?
    2. Are solutions well-behaved? I'm asking because no one can prove it for Navier-Stokes equation. Another reason is that Non-linear waves can develop singularities, and gluons fields are non-linear waves.
     
  2. jcsd
  3. Sep 5, 2010 #2

    tom.stoer

    User Avatar
    Science Advisor

    regarding 1: yes, e.g. instantons and merons are exact solutions of the theory; but due to the non-linearity they are of limited relevance as they can't be used to construct all solutions

    regarding 2: afaik no!

    regarding 3: afaik no proof exists

    general remark: classical solutions are of limited relevance; all the hard stuff in QCD is purely QFT; even instantons and merons are used in rare cases only; so it's really the QFT that needs to be solved and it seems that classical solutions do not really help. Maybe this is slightly different in lattice gauge theories ...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Questions about *classical* gauge field theory (Abelian and Non-Abelian)
  1. Question about gauge (Replies: 0)

Loading...