Where can I find the equations for the strong nuclear force?

[Reflector]

Where can I get the equations that describe the strong nuclear force between quarks/protons/neutrons? Are they not freely available? Thanks.

 

[quantumdude]

Where can I get the equations that describe the strong nuclear force between quarks/protons/neutrons? Are they not freely available? Thanks.

It's not a simple equation, like Newton's law of gravitation or Coulomb's law for electrostatics. It's a whole theory called Quantum Chromodynamics (QCD). It's freely available all right, but the problem is that no one knows how to solve it. Check it out http://theory.sinp.msu.ru/comphep_html/tutorial/node103.html.

 

[Nenad]

you can't solve the equations. They can only be reduced to a system of equations with too many variables and too little equations, kind of like general relativity.

 

[quantumdude]

you can't solve the equations. They can only be reduced to a system of equations with too many variables and too little equations,

No, that's not it. The problem is that gauge theories can only be solved perturbatively, and with QCD the running coupling constant is on the order of unity, so the perturbation series doesn't converge.

kind of like general relativity.

'Too many variables with too few equations' is not the problem with GR, either. In the case of GR, the equations are not exactly solvable because of their nonlinearity.

 

[Reflector]

Those equations in the link look too complicated for me. I was looking for something similar to the gravitational Force. Maybe I'm wasting my time anyway, I don't know. I have this theory but it didn't work out the way I wanted. Say, you have a right triangle and you expect on one side two values (say L) to have equal length (ie. L-L)... but instead you find that the second value is actually 10 x the value of the first value (ie 10L-L). Can it still be solved according to a logarithm function?

 

[quantumdude]

Those equations in the link look too complicated for me. I was looking for something similar to the gravitational Force.

The problem is that there isn't one. Newton's law of gravitation and Coulomb's law for electrostatics are classical (not quantum) relations, and they are applicable for sufficiently strong field intensities and sufficiently large distances. With QCD, there is only the short-range interaction, and there is no regime in which a classical approximation would be valid.

Maybe I'm wasting my time anyway, I don't know. I have this theory but it didn't work out the way I wanted. Say, you have a right triangle and you expect on one side two values (say L) to have equal length (ie. L-L)... but instead you find that the second value is actually 10 x the value of the first value (ie 10L-L). Can it still be solved according to a logarithm function?

I'm at a loss as to how a logarithm would enter into the analysis at all.

 

[Reflector]

I thought that the logarithm dealt with 10-1 ratios. I don't know how else to make sense of the observation... plus having a logarithm may have something to do with dark matter... how there's like a 10-1 ratio of it compared with normal matter. I don't know. This was an ambitious attempt to link the strong force with gravity, and getting the 10-1 ratio instead of a 1-1 ratio has to mean something...

 

[quantumdude]

I thought that the logarithm dealt with 10-1 ratios.

It does: An increase by one power of ten, is an increase by 1 on a log scale. But exactly what analysis do you plan to do on a right triangle with logarithms? Right triangles are solved with trig functions, not logs.

I don't know how else to make sense of the observation...

What observation? Being mistaken about the length of a side of a triangle by a factor of 10? That doesn't imply that you need logarithms, it implies that you need glasses.

plus having a logarithm may have something to do with dark matter... how there's like a 10-1 ratio of it compared with normal matter. I don't know.

There is no connection between logarithms and dark matter.

This was an ambitious attempt to link the strong force with gravity, and getting the 10-1 ratio instead of a 1-1 ratio has to mean something...

Well, I don't think you're putting any pressure on the string theorists just yet. I think you should keep studying physics to get the fundamentals down first.

 

[arivero]

Reflector, maybe you are looking for a force equation coming from a potential. Part of the problem is that it is not granted that you are going to be able to have a relativistic invariant potential for any force. The more effective trick is called Born approximation, and let's you to get a potential which approaches the real force.

Secondly, please take into account that the strong force between protons and neutrons is simply a residual of SU(3) force between quarks. So you need more more approximations. A very popular one is the OBE, One-Boson-Exchange approximation, where particles interact exchanging a nuclear boson, for instance a pion. Also empirical models are used, not coming from the fundamental theory.

Last, the whole colective of nucleons in a nucleus add to form a kind of well potential; this is approached with saxon-wood potential, or even with a square well.

 

[Olias]

I thought that the logarithm dealt with 10-1 ratios. I don't know how else to make sense of the observation... plus having a logarithm may have something to do with dark matter... how there's like a 10-1 ratio of it compared with normal matter. I don't know. This was an ambitious attempt to link the strong force with gravity, and getting the 10-1 ratio instead of a 1-1 ratio has to mean something...

Do the Words:Magnitude + Scale mean anything?

If so the wrong turning you took is evident

 

[Alem2000]

Hi, I wanted to as Tom a question. I havnt completed the introductory physics courses yet but since I saw the equation for the strong nuclear force I was wondering what the string theory equations look like. If you could please post them I would be greatful.

 

[Alem2000]

...and if I may add. What exactly can be done with the strong nuclear force equations...im confused, if they can't be solved than how are they relavant? Please keep in mind I am a beginner!

 

[arivero]

They (QCD+QED) are used in accelerator experiments, where only two particles are involved; there they are very accurate.

In the nucleus, they are only basis to create approximate models (One Boson Exchange etc) which in turn are reapproximated.

 

[quantumdude]

Hi, I wanted to as Tom a question. I havnt completed the introductory physics courses yet but since I saw the equation for the strong nuclear force I was wondering what the string theory equations look like. If you could please post them I would be greatful.

Have a look at this:

http://viswiz.gmd.de/~nikitin/course/node8.html

 

[quantumdude]

...and if I may add. What exactly can be done with the strong nuclear force equations...im confused, if they can't be solved than how are they relavant? Please keep in mind I am a beginner!

They can be approximately solved in certain regimes. The problem with QCD is that, for "normal" energies, the coupling constant is on the order of "1". This contrasts with the situation in QED, in which the coupling constant is 1/137, which means that graphs with a large number of vertices (and hence higher powers of the coupling constant) are supressed. Such is not the case with higher order QCD graphs.

But, at low energies, QCD can be approximated with Lattice QCD, in which spacetime is discretized (note: this is not quantum general relativity). And at high energies, the coupling constant drops down below "1", making a perturbation expansion possible. Both lattice QCD and perturbative QCD (pQCD) give good results in their appropriate regimes.

Confused? Me too...

 

[Alem2000]

Oh don't you worry Tom Mattson...I sure am confused...but also enamored! I can't waight to learn this stuff..not string theory but about the strong and weak nuclear forces.

The math I saw..what is it...i saw integrals and I think derivatives(or did I?). What is the mathematics used in strings...and by the way thanks for posting that.

 

[heardie]

the math used is hardcore - looks like a lot of tensor calculus to me