<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>On Thu, 28 Oct 2004, Doug Sweetser wrote:\n\n> I bought the DVD and looked for the elegant equations. The few I found\n> did not make a strong case for the thesis.\n\nThe document on PBS has been created for regular viewers, so it does not\ncover any math - except for potential anomalies in 1+1=2 and 31x16=496,\nand except for Einstein\'s equations and the Euler beta function (Veneziano\namplitude) which are not really explained. ;-) I thought it was\ncomprehensible that the document was not created for physics PhD students\nor professionals. :-)\n\n> > L.M.: First of all, the laws behind the Universe are not dumb.\n>\n> Perhaps instead of "dumb", backdoorstudent should have said something\n> about "no thought involved" or "necessarily automatic".\n\nIt was my statement, not backdoorstudent\'s statement, as we now explain in\ntwo other postings.\n\n> Fundamental particles are labeled that due to their simplicity.\n\nElementary particles are called elementary because according to the most\ncurrent theory that describes them (and their interactions), namely the\nStandard Model, they have no internal structure. In string theory, they\nwould not be quite elementary, but we tolerate the term anyway. ;-)\n\n> ... We don\'t understand all the rules or logic, ...\n\nWhich rules of logic do you precisely misunderstand? We may be able to\nhelp you. ;-)\n\n> but no particles are making tricky calculations very rapidly.\n\nApologies for I don\'t quite understand this sentence.\n\n> For me, the focus should be on Lagrange densities, ...\n\nThe whole of string theory probably cannot be written as a simple\nLagrangian density in spacetime.\n\n> L = (-g)^(1/2) R\n\nThis is the 1915 type of beauty, but in 2004 we\'re a bit further.\n\n> L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)\n\nThat\'s a 1864-style beauty.\n\n> Different symmetries are brought in in similar fashion. The aspect that\n> feels incomplete is why Nature decided to use U(1), SU(2), ...\n\n1969.\n\n> and SU(3) ...\n\n1974.\n\n> ... but not some other combination.\n\nWe can eliminate many other combinations because they would be anomalous,\nbut something is missing. String theory is the only framework with the\ncapacity to answer such questions about the gauge groups, but it has not\ndone it yet.\n\n> So Lubos, that brings me to a question for you. I would like to see one\n> of these "pretty long" Lagrangians in 11 dimensions.\n\nOnce again, local field theories with Lagrangians for a finite number of\nfields in spacetime are just approximations of string theory at long\ndistances. At general distances, string theory predicts an infinite number\nof new fields, phenomena, and their precise structure.\n\nThe only Lagrangian in large 11 dimensions worth your time is the\nLagrangian of 11-dimensional supergravity - which is more beautiful, in a\nphysics counting, than just general relativity - because it has not only\ngeneral covariance, but also local supersymmetry. But in a sense, it is\njust some Lagrangian - a generalization of your GR and Maxwell\'s system,\nplus some fermions. See e.g. the original paper by Cremmer+Julia+Scherk\n\nhttp://ccdb3fs.kek.jp/cgi-bin/img_index?7805106\n\nor one of its citations or the textbooks on SUGRA or string theory - for\nexample volumes II of Polchinski\'s "String Theory" (page 85) or\nGreen+Schwarz+Witten "Superstring theory".\n\nThe bosonic part of the Lagrangian has 11D version of \\sqrt(g).R, as in\nGeneral Relativity, plus |F(4)|^2, where F(4) is the completely\nantisymmetric tensor with 4 indices (4-form), plus C(3) /\\ F(4) /\\ F(4) / 6,\nwhere C(3) is the 3-form potential for the 4-form F(4). The last term is\ncalled the Chern-Simons term, and it is required by supersymmetry. There\nare also the fermionic terms for the gravitino - psi^a_\\mu with one spinor\nindex and one vector index (gravitino is spin 3/2, in the 4-dimensional\nlanguage). The gravitino psi also couples to the field strength F(4), and\nthere is also a quartic term of the form psi^4, with some contractions.\nAll this structure is completely determined by supersymmetry.\n\nThe exact physics of M-theory at all energies can also be described by a\nLagrangian - of the large N BFSS matrix model\n\nhttp://arxiv.org/abs/hep-th/9610043\n\n> Please try to label all the parts that go into it as I did for the\n> standard model Lagrangian. I realize this is an ongoing area of\n> research, so there is no consensus on which particular one to write\n> out, I just would like to see one of the 11D Lagrange densities as\n> part of my continuing education in string theory.\n\nThere is only one meaningful SUSY Lagrangian in 11 dimensions, and it is\njust too long to write it again, and therefore I referred to literature.\nRealistic models based on 11-dimensional M-theory are obtained by\ncompactifying the M-theory on a singular 7-dimensional manifold of G2\nholonomy.\n________________________________________________________ ______________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/384-9488 home: +1-617/868-4487 (call)\nWebs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^\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>On Thu, 28 Oct 2004, Doug Sweetser wrote:
> I bought the DVD and looked for the elegant equations. The few I found
> did not make a strong case for the thesis.
The document on PBS has been created for regular viewers, so it does not
cover any math - except for potential anomalies in [itex]1+1=2[/itex] and [itex]31x16=496,[/itex]
and except for Einstein's equations and the Euler [itex]\beta[/itex] function (Veneziano
amplitude) which are not really explained. ;-) I thought it was
comprehensible that the document was not created for physics PhD students
or professionals. :-)
> > L.M.: First of all, the laws behind the Universe are not dumb.
>
> Perhaps instead of "dumb", backdoorstudent should have said something
> about "no thought involved" or "necessarily automatic".
It was my statement, not backdoorstudent's statement, as we now explain in
two other postings.
> Fundamental particles are labeled that due to their simplicity.
Elementary particles are called elementary because according to the most
current theory that describes them (and their interactions), namely the
Standard Model, they have no internal structure. In string theory, they
would not be quite elementary, but we tolerate the term anyway. ;-)
> ... We don't understand all the rules or logic, ...
Which rules of logic do you precisely misunderstand? We may be able to
help you. ;-)
> but no particles are making tricky calculations very rapidly.
Apologies for I don't quite understand this sentence.
> For me, the focus should be on Lagrange densities, ...
The whole of string theory probably cannot be written as a simple
Lagrangian density in spacetime.
> [itex]L = (-g)^(1/2) R[/itex]
This is the 1915 type of beauty, but in 2004 we're a bit further.
> [itex]L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)[/itex]
That's a 1864-style beauty.
> Different symmetries are brought in in similar fashion. The aspect that
> feels incomplete is why Nature decided to use U(1), SU(2), ...
1969.
> and SU(3) ...
1974.
> ... but not some other combination.
We can eliminate many other combinations because they would be anomalous,
but something is missing. String theory is the only framework with the
capacity to answer such questions about the gauge groups, but it has not
done it yet.
> So Lubos, that brings me to a question for you. I would like to see one
> of these "pretty long" Lagrangians in 11 dimensions.
Once again, local field theories with Lagrangians for a finite number of
fields in spacetime are just approximations of string theory at long
distances. At general distances, string theory predicts an infinite number
of new fields, phenomena, and their precise structure.
The only Lagrangian in large 11 dimensions worth your time is the
Lagrangian of 11-dimensional supergravity - which is more beautiful, in a
physics counting, than just general relativity - because it has not only
general covariance, but also local supersymmetry. But in a sense, it is
just some Lagrangian - a generalization of your GR and Maxwell's system,
plus some fermions. See e.g. the original paper by Cremmer+Julia+Scherk
http://ccdb3fs.kek.jp/cgi-bin/img_index?7805106
or one of its citations or the textbooks on SUGRA or string theory - for
example volumes II of Polchinski's "String Theory" (page 85) or
Green+Schwarz+Witten "Superstring theory".
The bosonic part of the Lagrangian has 11D version of [itex]\sqrt(g)[/itex].R, as in
General Relativity, plus [itex]|F(4)|^2,[/itex] where F(4) is the completely
antisymmetric tensor with 4 indices (4-form), plus C(3) [itex]/\ F(4) /\ F(4) / 6,[/itex]
where C(3) is the 3-form potential for the 4-form F(4). The last term is
called the Chern-Simons term, and it is required by supersymmetry. There
are also the fermionic terms for the gravitino [itex]- \psi^a_\mu[/itex] with one spinor
index and one vector index (gravitino is spin [itex]3/2,[/itex] in the 4-dimensional
language). The gravitino [itex]\psi[/itex] also couples to the field strength F(4), and
there is also a quartic term of the form [itex]\psi^4,[/itex] with some contractions.
All this structure is completely determined by supersymmetry.
The exact physics of M-theory at all energies can also be described by a
Lagrangian - of the large N BFSS matrix model
http://arxiv.org/abs/http://www.arxi...hep-th/9610043
> Please try to label all the parts that go into it as I did for the
> standard model Lagrangian. I realize this is an ongoing area of
> research, so there is no consensus on which particular one to write
> out, I just would like to see one of the 11D Lagrange densities as
> part of my continuing education in string theory.
There is only one meaningful SUSY Lagrangian in 11 dimensions, and it is
just too long to write it again, and therefore I referred to literature.
Realistic models based on 11-dimensional M-theory are obtained by
compactifying the M-theory on a singular 7-dimensional manifold of G2
holonomy.
__{____________________________________________________________________ ________}
E-mail:
lumo@matfyz.cz fax: [itex]+1-617/496-0110[/itex] Web:
http://lumo.matfyz.cz/
eFax: [itex]+1-801/454-1858[/itex] work: [itex]+1-617/384-9488[/itex] home: [itex]+1-617/868-4487[/itex] (call)
Webs:
http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^