## mass gap and Yang Mills

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet 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\'ve been searching the internet and I haven\'t been able to\nfind a definition of the Yang-Mills mass gap that makes sense to me.\nHow can a wave moving at the speed of light have rest mass?\nIs this wave a wavefunction or some other theoretical construct?\nAnd why is such a wave required by theory?\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>I've been searching the internet and I haven't been able to
find a definition of the Yang-Mills mass gap that makes sense to me.
How can a wave moving at the speed of light have rest mass?
Is this wave a wavefunction or some other theoretical construct?
And why is such a wave required by theory?

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alistair wrote: > I've been searching the internet and I haven't been able to > find a definition of the Yang-Mills mass gap that makes sense to me. True, the fundamental degrees of freedom in Yang-Mills (the gluonic fieldstrength) are massless. However, if one would be able to calculate the spectrum of Yang-Mills at low energies (well under the QCD scale about 200 MeV if I'm not mistaken) one would expect to find no states at zero energy. This is the mass-gap, the spectrum of status starts at energies bigger than zero. > How can a wave moving at the speed of light have rest mass? The resolution of this problem is simple: If it has rest-mass it is not moving at the speed of light :-) > Is this wave a wavefunction or some other theoretical construct? > And why is such a wave required by theory? Wave-functions, states, it depends on the language you use. The mass gap seems necessary to proof confinement, since massless states would mediate long range forces (think electromagnetism) and that is in contradiction with a confining force. best, Jeroen



alistair wrote: > I've been searching the internet and I haven't been able to > find a definition of the Yang-Mills mass gap that makes sense to me. The book by Glimm and Jaffe makes good though demanding background reading. The mass gap appears in the form of correlation inequalities. > How can a wave moving at the speed of light have rest mass? The mass gap is a property of the theory, not of a wave function. Intuitively, it means that, in the rest frame of the total system, the ground state (=vacuum) is an isolated eigenstate of the Hamiltonian H, i.e., that the spectrum of H is a subset of {0} union $[E_1,inf]$. The largest $E_1$ with this property defines the mass gap $m_1=E_1/c^2.$ This would make proper sense for a nonrelativistic theory. For a relativistic theory one has to read between the lines and interpret everything in terms of suitable analogies, for lack of a consistent mathematical theory. The millenium problem essentially asks for a rigorous mathematical setting in which the above can be made precise and proved. See the section 'Is there a rigorous interacting QFT in 4 dimensions' in my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physics-faq.txt Arnold Neumaier

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