Covariant derivate same as normal derivative?

[vitaniarain]

hey, I'm getting really confused with something. If i have the covariant derivative of say, constant * exp(2f), is this equivalent to 2*constant*exp(2f) * cov.deriv. of f ?

 

[arkajad]

As a rule covariant derivatives are defined so as to satisfy the Leibniz rule. The formula for a covariant derivative of a composition of functions can be deduced from this rule.

What is your f? What kind of a covariant derivative? Sometimes, however, it can be a graded Leibniz rule (when you are playing with supersymmetry, for instance). Then one has to be more careful.

 

[vitaniarain]

thanks for the reply. f is a scalar field. what do u mean what kind of covariant derivative i didn't know there were many. this is in the framework of general relativity..

 

[arkajad]

thanks for the reply. f is a scalar field. what do u mean what kind of covariant derivative i didn't know there were many. this is in the framework of general relativity..

Covariant derivatives occur in the context of general relativity or in the context of gauge theories.