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Symmetry and range of interaction 
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#1
Jul2009, 07:07 PM

P: 4

I have just read a book. It said that: "if symmetry is exact, interaction is a long range". Could you explain me more detailed? Thanks!



#2
Jul2009, 08:58 PM

P: 980

You're going to need to provide a longer context.



#3
Jul2009, 09:28 PM

P: 16

Does it refer to gauge symmetry?
If gauge symmetry is exact, the gauge bosons are massless so interaction is long range; if gauge symmetry is broken, the gauge bosons get mass and interaction becomes short range. 


#4
Jul2109, 11:05 AM

Sci Advisor
P: 779

Symmetry and range of interaction
I think your book lied to you! 


#5
Jul2109, 02:45 PM

P: 546

It is, however, possible to create a quarkgluon plasma (if you're at high enough temperature and pressure), in which quarks no longer remain bound. Since there's no confinement here, it should be much clearer that the strong force is, in fact, longranged. 


#6
Jul2109, 07:23 PM

P: 2,828




#7
Jul2109, 07:38 PM

P: 980

Besides, it's important to maintain distinction of phases. Gluons, photons, etc. are massless in the absence of any other matter, including any potential condensates.
However, I think Phiphy managed to guess the OP's intent  good work sir :) For a first level understanding of things, I think it's fairly to say that exact gauge symmetry => massless bosons. It's a useful rule of thumb until you have to face reality :p 


#8
Jul2109, 08:54 PM

P: 16




#9
Jul2209, 12:38 PM

P: 4




#10
Jul2209, 01:06 PM

P: 527

The introduction of a mass causes a dropoff of the effective range of the mediated particle. Effectivel, the range drops as ~[tex]e^{x m}[/tex] (give or take a few parameters). For instance, a massive photon would give rise to a modified Coulomb potential that looks like: [tex]\frac{1}{r}e^{x m}[/tex]. For m=0, the exponential dropoff vanishes and we have longranged behavior again.



#11
Jul3009, 03:34 PM

P: 27




#12
Jul3009, 03:42 PM

P: 27




#13
Jul3009, 04:06 PM

P: 27




#14
Jul3009, 10:05 PM

P: 546

As for quarkgluon plasmas, I was under the impression that the consensus view was that they have, in fact, been created in heave atom collisions at RHIC. Finally, confinement, in and of itself, is not sufficient to say that the interaction is shortranged. It is, in fact, quite possible to write down a model of an SU(3) gauge theory in which the quarks are able to be separated to arbitrary distance (given, of course, that there's a way to give them sufficient energy). What is necessary is that all quarks in the model have mass much greater than the strong coupling scale of the theory (which, in QCD, is approximately the pion mass). In this case, the fragmentation of a bound state (which is what really restricts the range of the fundamental interaction in normal QCD) is suppressed by a factor of [itex]e^{m_q^{\phantom{q}2}/\Lambda^2}[/itex]. Models like this are generally referred to as "quirk" models. (See, for instance, http://arxiv.org/abs/0805.4642.) 


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