This is for the QFT-specialists

[marlon]

For some times I am having some problems with a few things in QFT. So please, i could use some clarification.

if we consider a quark-antiquark-pair in the QCD-vacuum (dual vacuum i mean, so no virtual quark antiquarks but magnetic monopoles bound in pairs like Cooperpairs) they are connected through a fluxtube.

Now when you consider moving quarks in such a vacuum it is stated that their mass depening on momentum (so this should be the kinetic part or the relativistic mass) is not zero but some positive integer which increases when the mass of the dual vacuum-particles increases.

This dynamical mass is also an effective mass , this means (i think) that the evolution of this mass is also (besides the momentum p) determened by the interactions of such quarks with the vacuum.

Is it ok to state that mass can be generated in such a way (i mean through these interactions) in QFT ?

Secondly, when we execute a Wick rotation in order to work with imaginary time right ? But what is the big advatage of that ?? What are the fysical implications?


I hope someone can help me out here
marlon

 

[Haelfix]

The real answer to the first question is a little bit subtle and involved, and part of topological field theory. Flux tubes in QCD in general are problematic, so the answer is also going to be ... not quite wrong. I'll get back to this at some point if I have time, and have a text available to make sure I am not making a mistake.

The second question is easy to state. Wick rotation changes a four dimensional pseudo riemanien path integral into a euclidean one. The prescription is to send t --> i t.

The reason this is attractive, is because mathematically the latter is much better defined than the former. Essentially what you have in the generic path integral, is a dangling imaginary phase that oscillates wildly off to infinity, and its very hard to get control off. Alternatively, you can think of wick rotation as a prescription for ordering your operators that makes them behave better. The real path integral is obtained by analytically continuing the euclidean path integral into the complex plane, and retrieving the 'information'. For whatever reason (and its still a bit of a mystery imo), field theory loves wick rotation for calculational purposes. What it 'means', other than a useful math trick, is anyone's guess.

 

[marlon]

thanx for your reply

i will be waiting for some more info on the first question...

marlon

 

[marlon]

RE : this is for QFT specialists

Hi, I will include the text in which i found this mysterious dynamical quarkmass. It is in chapter six. It is stated that dynamical quarkmass equals the averaged u and d -quak masses + some quantity sigma. I think this sigma represents some reference to the quark-gluon interaction right ? Some kind of a coupling constant.

Maybe somebody can get a more clear view on this.

it is a pdf-file ,on this site

http://arxiv.org/PS_cache/hep-ph/pdf/9312/9312350.pdf
greetz

marlon from belgium

 

[marlon]

I would like to ask my questions based on this text, so i will wait some time until anyone has read it , ok ?

This text is a nice work on quarkconfinement and its properties