I came across the following statement in this often-referenced paper on Einstein-Cartan theory (3rd page, right-hand column):(adsbygoogle = window.adsbygoogle || []).push({});

"In a space with torsion it matters whether one considers the potential of the electromagnetic field to be a scalar-valued 1-form or a covector-valued 0-form."

.. and the author then proceeds to list the resulting different behavior of torsion.

However, I am unaware of any difference between scalar-valued 1-forms and covector-valued 0-forms. In a 4d manifold are not both represented by the same four components? Are not both identical to the dual of the tangent vectors?

Perhaps I am not clear on the meaning of these terms. Can anyone here clarify the difference, if any, between a "scalar-valued 1-form" and a "covector-valued 0-form"?

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# Covectors not identical with 1-forms?

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