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http://en.wikipedia.org/wiki/Quantum_electrodynamics#Equations_of_motion

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- #1

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http://en.wikipedia.org/wiki/Quantum_electrodynamics#Equations_of_motion

- #2

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Did you say you don't remember seeing Dirac's equation with an interaction or Maxwell equations in Textbooks? Are sure about that? These equations are at the very heart of electromagnetism!

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What about QCD? Its equations of motion are the "Dirac equation" for QCD and "some equations for strong interaction"? Those I don't remember coming across.

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- #6

tom.stoer

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- A trivial example is the solution ψ=0, A=0 which is the starting point of perturbation theory.

- Another example is the so-called instanton

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

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edguy99

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* The Dirac equation can then be written as an equation coupling these two 2-spinors, each acting as a kind of ‘source’ for the other, with a ‘coupling constant’ M describing the strength of the ‘interaction’ between the two...

* More formally, break an electron field into two parts (left and right) as ψ=ψL+ψR

where ψL=(1/2)*(1−γ5)ψ and ψR=(1/2)*(1+γ5)ψ.

* These two massless fields, one left-handed and one right-handed, interact with coupling constant M equal to the mass of the electron.

These can be represented classically where 2 different things spinning are somehow held together by an interaction energy. The object you are looking at is no longer just a spinning ball, it could have multiple layers (2 in this case) that are spinning independently. That way, you can represent a larmour frequency of one axis around another and spin flips.

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Thanks all! But I'm still a little confused what the Euler-Lagrange equation for QCD gives?

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You should be able to derive them. Just write down the Lagrangian and start to differentiate it.

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You should be able to derive them. Just write down the Lagrangian and start to differentiate it.

That is true. However, it would require somewhat lengthy calculations and even more work to figure out what the equations actually mean and imply. In the end I fear that some problem would arise, since I have never come across a classical version of QCD.

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- #12

tom.stoer

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

- #13

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Okay, I was slightly vague. I meant a classical theory of the strong interaction, like Maxwell in EM. I don't quite follow your last sentence.

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

These instanton solutions are not exactly what I was asking, right? They are interesting, though.

- #14

Avodyne

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http://www.t39.ph.tum.de/T39_files/Lectures_files/StrongInteraction2011/QCDkap2.pdf

Eqs of motion are rarely used in QFT for the same reason that they are rarely used in QM: they're just not that useful for the quantities we're typically interested in.

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