Quantum mechanics

Mathematical physics

Anomalous magnetic dipole moment

Particle physics

Gauge boson

Gauge theory

Physics

Renormalization

Electron

Unitarity

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

We quantize a model with spontaneously broken symmetry in the asymmetrical gauge ${\ensuremath{\partial}}_{\ensuremath{\mu}}{A}^{\ensuremath{\mu}}=(\frac{{\ensuremath{\kappa}}^{2}}{m})\ensuremath{\Phi}$, where ${A}^{\ensuremath{\mu}}$ is the vector meson with mass $m$ and $\ensuremath{\Phi}$ is the gauge excitation field. We show that ${\ensuremath{\kappa}}^{2}$ can be identified as the mass parameter of the $\ensuremath{\Phi}$ field, in addition to the numerical parameter $\ensuremath{\xi}$ defined in the text. This implies that $\ensuremath{\Phi}$ is not a Goldstone boson. A renormalization gauge corresponds to any gauge with ${\ensuremath{\kappa}}^{2}$ finite. One can formally go over to the unitarity gauge by the limit ${\ensuremath{\kappa}}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$. 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 $\ensuremath{\xi}=1$ and ${\ensuremath{\kappa}}^{2}={m}^{2}$ is particularly convenient for finite calculations, (c) ambiguities may arise if the ${\ensuremath{\kappa}}^{2}=\ensuremath{\infty}$ is taken haphazardly, and (d) renormalization constants are gauge-dependent and in some cases can be defined only for certain values of ${\ensuremath{\kappa}}^{2}$.

Quantization and Gauge Freedom in a Theory with Spontaneously Broken Symmetry