# List of fundamental equations and constants of the standard model

• einKI
In summary, the conversation discusses the standard model and its fundamental equations and constants. The Lagrangian is mentioned as a way to describe interactions, but it is noted that there are also other forms of the Lagrangian with different notations and bases. It is also noted that the standard model includes about 19 free parameters that cannot be calculated from the theory and must be determined experimentally. The topic of quantum field theory is also mentioned, as well as the need for a complete understanding of the Lagrangian and its interpretation to get physical predictions. The conversation ends with a suggestion to consult the PDG for a list of free parameters and to do further research on quantum field theory to fully understand the topic.
einKI
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

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

einKI said:
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.

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, 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.

Hi

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

by
einKI

this seems interesting enuf

Last edited by a moderator:
This thread is 4 years old.

## 1. What is the standard model in physics?

The standard model is a theory that describes the fundamental particles and their interactions that make up the universe. It is currently the best explanation we have for the behavior of matter and energy at a microscopic level.

## 2. What are the fundamental equations in the standard model?

The fundamental equations in the standard model include the equations of quantum field theory, such as the Dirac equation and the Yang-Mills equations. These equations describe how particles interact with each other through the four fundamental forces: gravity, electromagnetism, strong nuclear force, and weak nuclear force.

## 3. What are the fundamental constants in the standard model?

The fundamental constants in the standard model include the speed of light, Planck's constant, the gravitational constant, and the fine structure constant. These constants are important in determining the behavior of particles and the strength of their interactions.

## 4. How is the standard model used in scientific research?

The standard model is used to make predictions and calculations in a wide range of scientific research, from particle physics to cosmology. It has been extensively tested and continues to be refined through experiments and observations.

## 5. Are there any limitations or criticisms of the standard model?

While the standard model has been incredibly successful in explaining many phenomena in the universe, it is not a complete theory. It does not include gravity and does not explain dark matter and dark energy. There are also some theoretical criticisms, such as the hierarchy problem and the lack of a unifying principle. Scientists continue to research and develop new theories to address these limitations.

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