How does one write the standard model Lagrangian in other smaller Lagrangian counterparts? Before electroweak symmetry breaking by the Higgs Mechanism:

$L_{EW} = L_{g} + L_{f} + L_{h} + L_{y}$


$ L_{g} $ describes the interaction between the three W particles and the B particle.

$ L_{g} = -W_{a}^{\muν}W_{\muν}^{a}/4 - B^{\muν}B_{\muν}/4$

$ L_{f} $ is the kinetic term for the Standard Model fermions.

$ L_{h} $ is the Higgs Field Lagrangian.

$ L_{y} $ gives the Yukawa interaction that generates fermion masses after the Higgs acquires a vacuum expectation value.

After electroweak symmetry breaking by Higgs mechanism:

$L_{EW} = L_{K} + L_{N} + L_{C} + L_{H} + L_{HV} + L_{WWV} + L_{WWVV} + L_{Y}$

What the terms mean can be obtained by a simple Google Search, as I will not list them out here.

My question is therefore this:

$ L_{SM} = \space???$

It consists of

terms of SM Lagrangian

How do I express these terms in their respective shorthand form? The first term $ -B^{\muν}B_{\muν}/4 $ happens to be the 2nd half of $ L_{g} $, so it is well understood if it was represented as $L_{U1}$?

How about the rest?

  • $\begingroup$ Related question on Quora. $\endgroup$ – Qmechanic Jul 19 '16 at 11:32
  • $\begingroup$ Yes, I've looked at it but it does not provide the specific terms of the Lagrangian and their association, so it was rather unsatisfactory. $\endgroup$ – Lagrangian Jul 19 '16 at 12:02


  • $\begingroup$ U(1), SU(2) and SU(3) terms are probably parts of other Lagrangian terms, as they are not Lagrangians themselves. $\endgroup$ – Lagrangian Jul 21 '16 at 5:29
  • 1
    $\begingroup$ @Lagrangian Refer to guage theory $\endgroup$ – Ariana Jul 21 '16 at 5:30

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