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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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- #3

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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

- #7

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.

- #8

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

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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.

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

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

- #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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