<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I am newly-subscribed to this group. In the past week I wrote two DRAFT\npapers on exactly the questions you asked here, which I attach. I have\ntried to reply a few times, and found out that attachments and symbols don\'t\nwork. So, I reply without the mathematics. If you wish to see these\npapers, please let me know and I\'d be happy to forward them.\n\nIn specific reply:\n\n> I hear occasionally talk about monopoles. How does a monopole term look\n> like in the Lagrangian if one were to exist? Also, is there a magnetic\n> monopole(s) analog for the weak or strong force?\n\nReinich and Wheeler some years ago developed a duality formalism based on\nthe Levi-Cevita formalism where one can rewrite Maxwell\'s equations in a\nform where the monopole equation looks like the charge equation, but with a\n"dual" field:\n\n\nMy first "quarks and monopoles" paper hypothesizes that the gluon fields of\nthe strong interaction are equivalent to the dual field tensor, but with\ncolor indexes. The QCD Lagrangian would then can be made to easily include\nthe monopole equation. If one makes this hypothesis, then the strong color\ncurrent for quarks turns out to be a monopole current. In other words,\nQUARKS ARE MAGNETIC MONOPOLES, and magnetic monopoles are quarks! We never\nobserve a free magnetic monopole because we never observe a free quark. (I\nuse caps, not to shout, but because I don\'t know if italics will get\nthrough.)\n\nSo, yes, in my view, there is a magnetic monopole analog in the strong\nforce: the quarks themselves ARE colored magnetic monopoles.\n\n>How do those look like\n> in the Lagrangian?\n\nI show monopoles in the Lagrangian of the above paper, using the duality\nformalism. But, I assume your question was directed to what the Lagrangian\nlooks like for the usual monopole term in terms of ordinary electric fields\nwith three "cycling" spacetime indexes.\n\nI spent considerable time trying to obtain a Lagrangian for this expression\njust as you are apparently trying to do, and found it difficult to do so\nother than via the field duals, which is what led me to hypothesize that the\ngluon fields of the strong interaction are equivalent to the dual field\ntensor in the first place.\n\nThe indirect answer to this question is dealt with in a second draft\n"dipoles" paper. If one continues forward with the hypotheses above and\ngeneralizes the Reinich and Wheeler duality formalism to first and third\nrank duals, then the cycling index monopole is actually an object which, In\nterms of gluon fields, I believe is a colored "electric dipole."\n\nThe corresponding magnetic object with cycling indexes, is the usual\nmonopole term related to the usual electromagnetic field tensor. In\nelectroweak theory, one introduces an non-abelian gauge group and then\nbreaks the symmetry. Non-zero terms similar to the gluon dipole terms\nremain as well. I interpret this as a "magnetic dipole."\n\nSO, short answer to your question in light of the above:\n\nI believe the strong interactions involve quarks, which are colored magnetic\nmonopoles, and gluons, which are colored electric dipoles. These are not\nobservable in our everyday experience and you\'d have to get inside a nucleon\nto "see" a magnetic monopole because it is the same as "seeing" a quark.\nElectroweak interactions involve electric monopoles and magnetic dipoles,\nwhich of course we do see in everyday experience.\n\nHope this helps. Let me know if you wish to see the papers.\n\nThanks for the opportunity to reply. I appreciate feedback.\n\nJay R. Yablon\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I am newly-subscribed to this group. In the past week I wrote two DRAFT
papers on exactly the questions you asked here, which I attach. I have
tried to reply a few times, and found out that attachments and symbols don't
work. So, I reply without the mathematics. If you wish to see these
papers, please let me know and I'd be happy to forward them.
In specific reply:
> I hear occasionally talk about monopoles. How does a monopole term look
> like in the Lagrangian if one were to exist? Also, is there a magnetic
> monopole(s) analog for the weak or strong force?
Reinich and Wheeler some years ago developed a duality formalism based on
the Levi-Cevita formalism where one can rewrite
Maxwell's equations in a
form where the monopole equation looks like the charge equation, but with a
"dual" field:
My first "quarks and monopoles" paper hypothesizes that the gluon fields of
the strong interaction are equivalent to the dual field tensor, but with
color indexes. The QCD Lagrangian would then can be made to easily include
the monopole equation. If one makes this hypothesis, then the strong color
current for quarks turns out to be a monopole current. In other words,
QUARKS ARE MAGNETIC MONOPOLES, and magnetic monopoles are quarks! We never
observe a free magnetic monopole because we never observe a free quark. (I
use caps, not to shout, but because I don't know if italics will get
through.)
So, yes, in my view, there is a magnetic monopole analog in the strong
force: the quarks themselves ARE colored magnetic monopoles.
>How do those look like
> in the Lagrangian?
I show monopoles in the Lagrangian of the above paper, using the duality
formalism. But, I assume your question was directed to what the Lagrangian
looks like for the usual monopole term in terms of ordinary electric fields
with three "cycling" spacetime indexes.
I spent considerable time trying to obtain a Lagrangian for this expression
just as you are apparently trying to do, and found it difficult to do so
other than via the field duals, which is what led me to hypothesize that the
gluon fields of the strong interaction are equivalent to the dual field
tensor in the first place.
The indirect answer to this question is dealt with in a second draft
"dipoles" paper. If one continues forward with the hypotheses above and
generalizes the Reinich and Wheeler duality formalism to first and third
rank duals, then the cycling index monopole is actually an object which, In
terms of gluon fields, I believe is a colored "electric dipole."
The corresponding magnetic object with cycling indexes, is the usual
monopole term related to the usual electromagnetic field tensor. In
electroweak theory, one introduces an non-abelian gauge group and then
breaks the symmetry. Non-zero terms similar to the gluon dipole terms
remain as well. I interpret this as a "magnetic dipole."
SO, short answer to your question in light of the above:
I believe the strong interactions involve quarks, which are colored magnetic
monopoles, and gluons, which are colored electric dipoles. These are not
observable in our everyday experience and you'd have to get inside a nucleon
to "see" a magnetic monopole because it is the same as "seeing" a quark.
Electroweak interactions involve electric monopoles and magnetic dipoles,
which of course we do see in everyday experience.
Hope this helps. Let me know if you wish to see the papers.
Thanks for the opportunity to reply. I appreciate feedback.
Jay R. Yablon
