Clearly, a mass term for a vector field would render the Lagrangian not gauge-invariant, but what are the consequences of this? Gauge invariance is supposed to be crucial for the renormalisation of a vector field theory, though I have to say I'm not entirely sure why.
As far as removing unphysical degrees of freedom - why isn't the time-like mode $A_0$ a problem for massive vector bosons (and how does gauge invariance of the Lagrangian ensure that this mode is unphysical for gauge bosons)?
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