It is well known that the product rule for the exterior derivative reads(adsbygoogle = window.adsbygoogle || []).push({});

[tex]d(a\wedge b)=(da)\wedge b +(-1)^p a\wedge (db),[/tex]where a is a p-form.

In gauge theory we then introduce the exterior covariant derivative [tex]D=d+A\wedge.[/tex]What is then D(a ∧ b) and how do you prove it?

I obtain

[tex]D(a\wedge b)=d(a\wedge b)+A\wedge a \wedge b=(da)\wedge b +(-1)^p a\wedge (db)+A\wedge a \wedge b,[/tex]

which is neither (Da) ∧ b +(-1)^{p}a ∧ (Db) nor (Da)∧ b + a∧ (Db). I have, however, seen the latter been used without proof.

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

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

# I Product rule for exterior covariant derivative

Have something to add?

Draft saved
Draft deleted

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