Broken-phase spectrum of the Abelian Higgs model ($m_h^2=\lambda {\eta }^2,m_A^2=2e^2{\eta }^2$)

For $|D\Phi {|}^2-\lambda (|\Phi {|}^2-{\eta }^2{)}^2/4$, write $\Phi =(\eta +h/\sqrt{2})e^{i\theta }$ and absorb $\partial \theta /e$ into the vector field. The quadratic Lagrangian has a real scalar of mass $m_h=\sqrt{\lambda }\eta$ and a vector of mass $m_A=\sqrt{2}e\eta$. The two scalar plus two massless-vector polarizations in the symmetric phase become one radial scalar plus three massive-vector polarizations. The removed phase supplies the longitudinal mode; local vortices retain global winding and quantized flux.

// Target: cosmology.bigb