The equation is not literally correct. The single terms labeled Maxwell-Yang-Mills, Dirac, and Yukawa, are standing in for whole families of terms from the standard model lagrangian, a version of which you can see on page 1 here.
The "F^2" term, which comes from electrodynamics, should really be more like "trace(G^2) + trace(W^2) + B^2", where G is for gluons, and W and B are for the weak and hypercharge gauge fields before symmetry is broken by the Higgs. (The paper contains a further "trace(G G~)", a "theta term" which ought to exist according to the rules of lagrangian construction, but whose coefficient appears to be very close to zero in the real world.)
There is a single Dirac term in the picture, but in the paper I cite, you will see an analogous term for each of Q (left-handed quarks), U (right-handed up-type quarks), D (right-handed down-type quarks), L (left-handed leptons), E (right-handed charged leptons). In Q and L, the left-handed quarks and the left-handed leptons of each generation are treated as a single object that interacts with the weak bosons, whereas the right-handed quarks (e.g. up and down) and right-handed leptons (e.g. electron and electron-neutrino) are regarded as separate.
[For clarity I will emphasize that, in the standard model, there is a left-handed part and a right-handed part to each fermion, except for the neutrinos, which in the original standard model are purely left-handed. (That would make the neutrinos massless, so this aspect of the SM needs to be extended but we don't know exactly how.) So e.g. up quark has a left-handed part and a right-handed part, but the left-handed part of the up quark is bundled with the left-handed part of the down quark, into the combined left-handed quark field Q, whereas the right-handed parts remain alone as U and D.]
Also, there is a subscript i that runs from 1 to 3, because there is a Q,U,D,L,E in each particle generation. Also, the original Dirac term is just a kinetic term for the fermion, but the D-with-a-slash means that the so-called "long derivative" or "covariant derivative" is being used, which also includes the interactions of the fermions with the G,W,B fields.
Similarly, the single Yukawa term in the picture really stands for the three interaction terms QUH, QDH, LEH (as they are written in the paper), and the "lambda" coefficient actually stands for a 3x3 matrix of "yukawa couplings", which form the link between the left-handed and right-handed fermions (coupling Q to U and Q to D, and also L to E), thereby generating the masses and the weak-force mixings (the latter, because the Higgs field has an electroweak charge).
R in the picture is the Ricci scalar, which appears in the Einstein-Hilbert action for general relativity. So that part introduces gravity. The final two terms are the kinetic and potential terms for the Higgs field.
This post imported from StackExchange Physics at 2014-03-24 03:31 (UCT), posted by SE-user Mitchell Porter
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