A Why do we use covariant formulation in classical electrodynamics?

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The discussion centers on the preference for covariant formulation in writing Maxwell's equations in classical electrodynamics. Covariant formulation utilizes tensors, allowing for a more natural representation of physical laws, particularly through the Faraday tensor as an exact two-form. While both covariant and contravariant formulations exist, the covariant approach is often favored for its consistency with the principles of relativity. Resources like Vol. 2 of Landau and Lifshitz are recommended for further understanding, as they provide a relativity-first perspective on classical electrodynamics. Covariance is highlighted as a key characteristic of equations derived from the least-action principle.
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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)?
 
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Using metric tensor a covariant formula is written as a contra variant formula and vice versa.
 
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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.
 
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m_prakash02 said:
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.
 
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Dale said:
“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?
 
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.
 
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covariance is a common feature of least-action-principle generated equations
 
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