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"?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Covectors not identical with 1-forms?

**Physics Forums | Science Articles, Homework Help, Discussion**