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mass gap and Yang Mills |
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| Aug31-04, 02:40 PM | #1 |
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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"> 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? |
| Sep1-04, 04:05 AM | #2 |
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<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>\nalistair wrote:\n\n> I\'ve been searching the internet and I haven\'t been able to\n> find a definition of the Yang-Mills mass gap that makes sense to me.\n\nTrue, the fundamental degrees of freedom in Yang-Mills (the gluonic\nfieldstrength) are massless. However, if one would be able to calculate the\nspectrum of Yang-Mills at low energies (well under the QCD scale about 200\nMeV if I\'m not mistaken) one would expect to find no states at zero energy.\nThis is the mass-gap, the spectrum of status starts at energies bigger than\nzero.\n\n> How can a wave moving at the speed of light have rest mass?\n\nThe resolution of this problem is simple: If it has rest-mass it is not\nmoving at the speed of light :-)\n\n> Is this wave a wavefunction or some other theoretical construct?\n> And why is such a wave required by theory?\n\nWave-functions, states, it depends on the language you use. The mass gap\nseems necessary to proof confinement, since massless states would mediate\nlong range forces (think electromagnetism) and that is in contradiction\nwith a confining force.\n\nbest,\nJeroen\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>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 |
| Sep1-04, 03:23 PM | #3 |
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<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>alistair wrote:\n> I\'ve been searching the internet and I haven\'t been able to\n> find a definition of the Yang-Mills mass gap that makes sense to me.\n\nThe book by Glimm and Jaffe makes good though demanding background reading.\nThe mass gap appears in the form of correlation inequalities.\n\n\n> How can a wave moving at the speed of light have rest mass?\n\nThe mass gap is a property of the theory, not of a wave function.\nIntuitively, it means that, in the rest frame of the total system,\nthe ground state (=vacuum) is an isolated eigenstate of the Hamiltonian H,\ni.e., that the spectrum of H is a subset of {0} union [E_1,inf].\nThe largest E_1 with this property defines the mass gap m_1=E_1/c^2.\n\nThis would make proper sense for a nonrelativistic theory.\nFor a relativistic theory one has to read between the lines and interpret\neverything in terms of suitable analogies, for lack of a consistent\nmathematical theory. The millenium problem essentially asks for a\nrigorous mathematical setting in which the above can be made precise\nand proved.\n\nSee the section \'Is there a rigorous interacting QFT in 4 dimensions\'\nin my theoretical physics FAQ at\nhttp://www.mat.univie.ac.at/~neum/physics-faq.txt\n\n\n\nArnold Neumaier\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>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 [itex][E_1,inf][/itex]. The largest [itex]E_1[/itex] with this property defines the mass gap [itex]m_1=E_1/c^2.[/itex] 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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