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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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- Thread starter einKI
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- #1

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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

- #2

Science Advisor

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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.

- #3

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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

- #4

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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).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.)

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.

- #5

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

For instance there's 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.

- #6

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Hi

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

by

einKI

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

by

einKI

- #7

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this seems interesting enuf

- #8

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Hi,

Try wikipedia - equations seem correct to me;

http://en.wikipedia.org/wiki/Standard_Model_(mathematical_formulation [Broken])

http://en.wikipedia.org/wiki/Standard_Model

Try wikipedia - equations seem correct to me;

http://en.wikipedia.org/wiki/Standard_Model_(mathematical_formulation [Broken])

http://en.wikipedia.org/wiki/Standard_Model

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