Boson Propagator Derivation

[Jay R. Yablon]

Dear friends,

I have been working for several months to derive an exact solution for
non-Abelian Yang-Mills gauge theory. I believe I am now able to achieve
this objective.

Attached is the two-page introduction to a paper I will be writing on
this topic:

http://home.nycap.rr.com/jry/Papers/Yang-Mills-2.0.pdf

There is nothing new or speculative in the material at this link; I am
simply presenting my understanding of a well-known line of calculation
as a baseline for presenting the corresponding exact calculation for
Yang-Mills theory, and am asking for others to review whether I have
this piece right.

I have two questions:

1) Is this introduction accurate on its own terms; that is, are the
calculations and is the discussion an accurate presentation of what is
known?

2) Am I correct in understanding that when people speak about "solving"
or "quantizing" Yang-Mills theory, they are referring to developing an
exact line of calculation which mirrors the calculation in this
introduction, for a non-Abelian theory SU(N) of any N>=2, without, for
example, splitting the Lagrangian into the quadratic terms and all
remaining terms and thereby having to deal with gauge fixing, ghost
fields, etc., and without, for example, needing to employ lattice gauge
theory and its associated problems with Lorentz and rotational
invariance?

Thanks,

Jay.
_____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com
co-moderator: sci.physics.foundations

[Kay zum Felde]

Hi Jay,

I've just red the introduction of your paper and the rest of your paper til you finish the decomposition of the FF-interaction part with the the action S of the path-integral.

Your questions: to 1) This depends on the journal, where you want to publish this. The presentation appears to be correct, but if you read articles from different journals, there's sometimes taken more attention to explanations of the mathematical formalisms. You tend to overwhelm people with mathematical procedures. You don't have to show every step of your mathematical proofs. It's better to discover a balance of derivations of formulas. Don't just show the math. People can compute! Its a hard work, but more accurate is it to explain in words what you've done to yield to the results. And don't overwhelm people with details. Its also hard work, but you need to find the important steps towards your results. If the results are well-known, you can reference to the papers and explain what is needed for your work. Even your own calculations need to be written down with every single step. Again, try to find a 'bridge' between the important steps and fill the 'bridge' with concise and precise descriptions of what you do, like approximations and if needed physical descriptions.

to 2)

As I understand 'quantizing' a quantum field theory is finding the general momentums and general 'positions' and their commutation relations. In quantum field theories usually this is a problem because the generalized momentum with respect to the time derivative vanishes. This is called a primary constraint and there are also secondary constraints. These led to the Faddeev-Popov, BRST formalisms. You find more on this in S. Weinberg I and II (chapter 8 and 15,16).

greetings Kay

[Kay zum Felde]

Hi Jay,

I am not an expert on Feynman formalism, so I cannot yet check, if your quantizing procedure is correct (I shall try to get familiar with Feynman formalism, so that I shall give comments), but there‘s a good book available on the net (it‘s for free: Warren Siegel: arXiv:hep-th:9912205, 885 pages)

Regards

Kay