Differential form or differential form field?

Question

When discussing differential forms is it necessary to stick the word “field” on the end , such as “1-form field”, or “2-form field” in a similar fashion to vector and vector field? Or is, in the context of forms, the use of “field” redundant? Thanks.

Answer 1

Hardly anybody uses the word “field” in this context. Already when you say differential form, it's clear that it must be a field, since in order for the concept of derivative to be interesting, the quantity in question must vary from point to point.