# Basic question in electromagnetic duality

In electromagnetic duality, where does this relation come from?

$$\overrightarrow{E} \rightarrow \cos \alpha\overrightarrow{E} - \sin \alpha\overrightarrow{ B}$$ $$\overrightarrow{B} \rightarrow \cos \alpha\overrightarrow{B} + \sin \alpha\overrightarrow{ E}$$ I was familiar with $E \rightarrow B$ and $B \rightarrow -B$ but not with the one above.

• Could you provide more context? For example, where have you seen such a relation? (e.g., book, journal, etc) What is $\alpha$ here? – Kyle Kanos Dec 10 '14 at 17:58
• Yes of course, arxiv.org/abs/hep-th/9506035 p. 1 He said that In ordinary Maxwell spacetime a Hodge duality rotation is an action of SO(2) and then he placed the 2 equations I wrote above @KyleKanos – Fluctuations Dec 10 '14 at 18:08
• – Qmechanic Dec 10 '14 at 18:26