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I'm not sure if someone's already asked this before, but I was wondering, in field theory,

  1. when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In particular, in Wikipedia, the regulator of Pauli-Villars is said to be as such.

  2. Moreover, as a consequence of not being gauge covariant, the Wikipedia article says that this regulator can't be used in QCD. How to see the link between not being gauge covariant and QCD here? And, why can one use it in QED then?

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Hi Joman - could you split this post into two separate ones for your two questions? –  David Z Jun 8 '12 at 17:13
    
Hi David, I asked both together because I read them in the same sentence. So I would like to understand how the whole picture fit together. Is that Ok? –  Joman Jun 8 '12 at 17:22
    
Well, I suppose so. If you have two questions that are closely related then it's fine to put them in the same post. It just wasn't clear to me that these two are that closely related. So just as a suggestion, it might help if you could reword these to make that more clear. –  David Z Jun 8 '12 at 17:36
    
Ok, I'll try my best. –  Joman Jun 8 '12 at 17:43
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