Why do we use covariant formulation in classical electrodynamics?

[m_prakash02]

TL;DR Summary

Why exactly do we use only covariant formulation to write Maxwell's equations? Is there a specific reason?

I am a graduate physics student currently studying electrodynamics as a core paper. I want to know why exactly do we use only covariant formulation for writing Maxwell's equations? Or do we also use contravariant formulation (i.e., if something like that even exists)?

 

[anuttarasammyak]

Using metric tensor a covariant formula is written as a contra variant formula and vice versa.

 

[vanhees71]

I'd say the most "natural" understanding of the Faraday tensor is as an exact two-form,
$$F=\mathrm{d} \wedge A,$$
where the four-potential $A$ is understood as a one-form.

 

[Dale]

TL;DR Summary: Why exactly do we use only covariant formulation to write Maxwell's equations? Is there a specific reason?

I want to know why exactly do we use only covariant formulation for writing Maxwell's equations? Or do we also use contravariant formulation (i.e., if something like that even exists)?

“Covariant formulation” just means using tensors. You can use both covariant and contra variant tensors as needed.

 

[m_prakash02]

“Covariant formulation” just means using tensors. You can use both covariant and contra variant tensors as needed.

Thanks for the reply! Could you please suggest me some resources for further reading?

 

[vanhees71]

The best "relativity-first approach" to classical electrodynamics imho is Vol. 2 of Landau and Lifshitz (Classical Field Theory). It's also a very nice intro to General Relativity.

 

[wrobel]

covariance is a common feature of least-action-principle generated equations