Tuesday, 1 September 2020

quantum electrodynamics - Faddeev-Popov Gauge-Fixing in Electromagnetism


Reading section 9.4 in Peskin, I am wondering about the following:


The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero.


To "fix" this, we recognize that anyway we would not have liked to get contributions from pure-gauge field configurations, because field-configurations in the same gauge-orbit correspond to identical physical field configurations. Ultimately, we would like to make a functional integral which ranges over only distinct gauge-orbits, taking each time only one representative from each gauge orbit.


The way to do this technically is to insert a functional-delta function into the functional integral, where this delta function is always zero unless the field configuration obeys a particular gauge-condition, which is non-zero only once in each gauge-orbit.


So far, so good.


However, then Peskin chooses as the gauge condition the Lorenz gauge condition. I'm wondering: why is that valid? The Lorenz gauge condition does not completely fix the gauge: one can still make further gauge transformations by harmonic functions.


What gives?





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