A. Zee, Quantum Field Theory in a Nutshell · Problem VII.1.1

Field Theory Redux

Physics — QFT

Problem

The gauge choice in the text preserves Lorentz invariance. It is often useful to choose a gauge that breaks Lorentz invariance, for example, f(A)=nμAμ(x)f(A) = n^\mu A_\mu(x) with nn some fixed 4-vector. This class of gauge choices, known as the axial gauge, contains various popular gauges, each of which corresponds to a particular choice of nn. For instance, in light-cone gauge, n=(1,0,0,1)n = (1, 0, 0, 1), in space-cone gauge, n=(0,1,i,0)n = (0, 1, i, 0). Show that for any given A(x)A(x) we can find a gauge transformation so that n⋅A(x)=0n \cdot A(x) = 0.

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