# List of fundamental equations and constants of the standard model

## Main Question or Discussion Point

Hi

Is there anywhere a list of all constants (with their values) and fundamental
equations (which can not be constructed from any other equations) of
the standard model?

thx
einKI

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Haelfix
http://cosmicvariance.com/2006/11/23/thanksgiving

You'll find a few other forms of the sm lagrangian (sometimes before sometimes after electroweak symmetry breaking), notation will change sometimes, and the basis will change sometimes. But there it is.

Upon quantizing this theory, it leads to all the familiar properties we know and love about the real world.

Hi

thx for that however I have to ask some questions about it.

The Lagrangian describes how a system acts at a given action but
it doesn't describe which input you have to the action.
I mean in classical mechanics you can say well I have a ball with
mass m and radius r and use the Lagrangian to calculate how it reacts
at a force etc..
Or short it describes only the interactions.

But in the standard model there are only certain combinations of
values possible so I can have an electron of mass 0.511 MeV and charge -1
or a quark but I can't say well I want a particle with mass 0.2MeV.
So to have a complete description of the standard model shouldn't there
be a description of the fundamental particles?

And should furthermore not be at last Heisenbergs uncertainty principle
be included to get the measurement problem?

Or I am getting something fundamental wrong here?

thx
einKI

nrqed
Homework Helper
Gold Member
Hi

thx for that however I have to ask some questions about it.

The Lagrangian describes how a system acts at a given action but
it doesn't describe which input you have to the action.
I mean in classical mechanics you can say well I have a ball with
mass m and radius r and use the Lagrangian to calculate how it reacts
at a force etc..
Or short it describes only the interactions.

But in the standard model there are only certain combinations of
values possible so I can have an electron of mass 0.511 MeV and charge -1
or a quark but I can't say well I want a particle with mass 0.2MeV.
So to have a complete description of the standard model shouldn't there
be a description of the fundamental particles?

(aside: the expression given in the link has no Higgs boson. Strictly speaking, this is a non-viable theory because it is non-renormalizable (which is ok if one thinks of the SM as an effective field theory). One should really provide the full Standard Model, including the Higgs terms.)
There are about 19 free parameters in the Standard Model (which has massless neutrinos) with an extra 10 parameters if one includes neutrino masses. Those parameters can not be calculated from the theory, they have to be determined experimentally. Among those parameters are the so-called Yukaway couplings which determine the masses of the particles as well as the coupling constants (such as the electric charge).
And should furthermore not be at last Heisenbergs uncertainty principle
be included to get the measurement problem?

Or I am getting something fundamental wrong here?

thx
einKI
Well, it is not enough to simply give a Lagrangian to do physics! One must as well say what to do with it. In classical physics, one uses the principle of least action to get the dynamics of a system from a Lagrangian. In relativistic field theory, there is a well-defined procedure to get from a Lagrangian (or, more specificaly, from a Lagrangian density) such as the one given in the link to physical predictions (canonical quantization or the path integral formalism) and this procedure includes the Heisenberg uncertainty principle. This is the topic of quantum field theory.

So there are 3 pieces to give: the langrangian, the parameters in the lagrangian, and how to use the lagrangian to get physical results.

Haelfix
For a list of the free parameters of the standard model, your best bet is the PDG as they have the most up to date, experimentally fitted data in the world.

For interpreting just what that Lagrangian means and how to get predictions (say cross sections).. Well, thats quite a hefty undertaking if you've never seen it before. Its a good two term graduate level course.

For instance theres another form of that lagrangian one often sees with 'counterterms' for one loop calculations (more or less doubling the size of the equations), and sometimes ones with manifest ghost terms. It would be a complete mystery unless you know some QFT.

Hi

Thank you both for the answers. It clarified a lot for me.

by
einKI

this seems interesting enuf

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