Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 313 / 2 / v

Table of contents
- Solution v

Solution

For Maxwell theory the group is Abelian, so write

J = e^{χ}

. The reduced equation loses its commutators and becomes

\partial_{w} \partial_{\overset{w}{ˉ}} χ + \partial_{z} \partial_{\overset{z}{ˉ}} χ = 0.

Since the Euclidean Laplacian is

Δ_{R^{4}} = 4 (\partial_{w} \partial_{\overset{w}{ˉ}} + \partial_{z} \partial_{\overset{z}{ˉ}}),

the anti-self-dual Maxwell equations in this gauge are equivalent to

Δ_{R^{4}} χ = 0 .

 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