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.
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1I think "field" is redundant. A differential form is a particular type of tensor field, as I understand it. A differential form assigns an alternating $k$-tensor to each point on a manifold. – littleO Sep 24 '19 at 07:37
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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.
Hans Lundmark
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Hubbard and Hubbard in Vector Calculus, Linear Algebra, And Differential Forms, and Frankel in The Geometry of Physics both refer to form fields. – Peter4075 Sep 24 '19 at 07:52
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@Peter4075: Fair enough, I've moderated my statement a little! :-) – Hans Lundmark Sep 24 '19 at 07:54