 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2025

Paper 301

Put $\widetilde c=\widetilde a+\widetilde b$. Substituting the <transverse-longitudinal decomposition> $V_\mu=A_\mu+\partial_\mu\pi$ and integrating cross terms by parts gives
$$
\mathcal L\simeq
\widetilde a A_\mu\Box A^\mu+m^2A_\mu A^\mu
-\widetilde c(\Box\pi)^2+m^2\partial_\mu\pi\partial^\mu\pi.
$$
The equations are
$$
(\widetilde a\Box+m^2)A_\mu=0,
\qquad
\Box(\widetilde c\Box+m^2)\pi=0,
$$
together with $\partial_\mu A^\mu=0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 2 / b / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 2 / b / i / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 2 / b / i / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)