Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 37D / c

Table of contents
- Solution c

Solution

Take the divergence of the field equation. Commuting derivatives and antisymmetry of

F^{μν}

give

\partial_{ν} \partial_{μ} F^{μν} = 0.

Current conservation then yields

- m^{2} \partial_{ν} A^{ν} = - μ_{0} \partial_{ν} J^{ν} = 0.

For

m > 0

,

\partial_{μ} A^{μ} = 0.

This is the Lorenz constraint in Proca theory; it follows dynamically rather than being a gauge choice.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version