Quantization and Gauge Freedom in a Theory with Spontaneously Broken Symmetry

We quantize a model with spontaneously broken symmetry in the asymmetrical gauge ∂_μA^μ=(κ²m)Φ, where A^μ is the vector meson with mass m and Φ is the gauge excitation field. We show that κ² can be identified as the mass parameter of the Φ field, in addition to the numerical parameter ξ defined in the text. This implies that Φ is not a Goldstone boson. A renormalization gauge corresponds to any gauge with κ² finite. One can formally go over to the unitarity gauge by the limit κ²→∞. However, this limit should be taken with extreme care, so as not to interfere with the limits of internal-loop integration. Several examples, including the anomalous magnetic moment of an electron, are given to illustrate that (a) physical quantities are gauge-invariant, (b) the gauge with ξ=1 and κ²=m² is particularly convenient for finite calculations, (c) ambiguities may arise if the κ²=∞ is taken haphazardly, and (d) renormalization constants are gauge-dependent and in some cases can be defined only for certain values of κ².