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In Lattice, one cannot calculate gauge non-invariant quantities, such as the quark mass. This is because one averages over the gauge and gets 0.

One way to get around the issue is to fix the gauge. But the resulting quark mass will be gauge dependent. It is hard to interpret the meaning of this quantity, as free quarks cannot be found in nature. While quarks are confined, electrons are not. It is of course possible that while the Lattice calculation is gauge dependent, the final result is not.

However, a Lattice theorist recently told me that "it is known that the physical mass of the electron is a gauge dependent quantity. And what we measure in the lab (using spectrometer for example) is not the electron's mass". This is somewhat surprising to me. I did some search and couldn't find any references on it. Can someone comments on this issue?

Related questions:

References:

  • Ward, B. F. L. "On gauge invariance of the renormalized Z $^{0} $ rest mass." Phys. Lett. B 296.IC-91-161 (1991): 209-212.
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  • $\begingroup$ Related. "What we measure in the lab is not the electron's mass" is pointlessly oracular. It is a mass that CODATA fixes just fine. $\endgroup$
    – Cosmas Zachos
    Commented Feb 27, 2018 at 23:03
  • $\begingroup$ I would ask for an explicit demonstration that a gauge transformation can alter either the observed mass or the bare mass. It's my understanding that such transformations can only fiddle with the metric of the functional integral, but I don't know how gauge transformations interact with renormalization. $\endgroup$
    – Sean E. Lake
    Commented Feb 28, 2018 at 0:53
  • $\begingroup$ You were told wrong--if you are relating the verbatim statements. Electrons are asymptotic states and physical observables such as masses are gauge invariant, unlike Green's functions/propagators and much of the renormalization procedure. In QED, even running electron masses are gauge invariant. I don't understand why you are using lattice gauge theory (normally utilized for QCD, where the fields are not physical asymptotic states) to discuss electron masses and QED.... $\endgroup$
    – Cosmas Zachos
    Commented Feb 28, 2018 at 14:52
  • $\begingroup$ @CosmasZachos Thank you for the reply - I see your point. I used lattice QCD because our conversation started with it and I guess my mind was stuck with it for a while. I was wondering if Lattice QCD can explain confinement. I always get confusing answers from these conversations, this one [GI of electron mass] included. $\endgroup$
    – Yang
    Commented Feb 28, 2018 at 23:49
  • $\begingroup$ Lattice QCD motivates and confirms confinement--I'm not sure it completely proves or "explains" it... But that's a different question, no? $\endgroup$
    – Cosmas Zachos
    Commented Mar 1, 2018 at 1:39

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