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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 $1+1=2$ and $31x16=496,$ and except for Einstein's equations and the Euler $\beta$ 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. > $L = (-g)^(1/2) R$ This is the 1915 type of beauty, but in 2004 we're a bit further. > $L = -(d^u A^v - d^v A^u)(d_u A_v - d_v A_u)$ 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 $\sqrt(g)$.R, as in General Relativity, plus $|F(4)|^2,$ where F(4) is the completely antisymmetric tensor with 4 indices (4-form), plus C(3) $/\ F(4) /\ F(4) / 6,$ 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 $- \psi^a_\mu$ with one spinor index and one vector index (gravitino is spin $3/2,$ in the 4-dimensional language). The gravitino $\psi$ also couples to the field strength F(4), and there is also a quartic term of the form $\psi^4,$ 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: $+1-617/496-0110$ Web: http://lumo.matfyz.cz/ eFax: $+1-801/454-1858$ work: $+1-617/384-9488$ home: $+1-617/868-4487$ (call) Webs: http://schwinger.harvard.edu/~motl/ http://motls.blogspot.com/ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^