Use <unitary gauge> and write $\phi=v+h/\sqrt2$. The quadratic Lagrangian contains
$$
\frac12(\partial h)^2-\lambda v^2h^2+e^2v^2A_\mu A^\mu.
$$
Thus the radial Higgs excitation is a spin-zero particle with $m_h^2=2\lambda v^2$, while the gauge boson is a massive spin-one particle with $m_A^2=2e^2v^2$. The phase of $\phi$ is the <Goldstone boson> eaten by the <Higgs mechanism> to supply the longitudinal polarization of $A_\mu$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 305 / 1 / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-305/1/i/solution