# Physics interpretation of integrals of differential forms

1. Oct 27, 2014

### davi2686

Be a vector field $\vec{F}=(f_1,f_2,f_3)$ and $\omega^k_{\vec{F}}$ the k-form associated with it , i know if i do $\int \omega^1_{\vec{F}}$ is the same of a line integral and $\int \omega^2_{\vec{F}}$ i obtain the same result of $\int \int_S \vec{F}\cdot d\vec{S}$, wich is the flux of a vector field in a surface, so something like $\int \omega^k_{\vec{F}}$ have some physics interpretation like de flux of a vector field in R^k at a hypersurface? (sorry if i talk a nonsense).

2. Nov 1, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Nov 3, 2014

### davi2686

sorry at the moment i can't think another way to put what i need

4. Nov 5, 2014

### JorisL

I think you have the right idea. Your English makes it a little more difficult.

However I would advise you to just try some examples.
What helped me a lot, really A LOT.
With this and other issues relating to differential forms was considering electromagnetism and explicitly identify the equivalence between Maxwell's equations and the differential form notation.
Integrals show up when considering electric (and magnetic) charges.

Do you think you could do such a thing?

5. Nov 6, 2014

### lavinia

Differential forms are the mathematical objects for which it makes sense to integrate over an oriented volume. There are many examples in Physics but the idea is general and may not apply to a physical system in a particular instance.

It is important to understand what it means to integrate over an oriented volume by itself independently of Physics. But Physics examples are helpful in clarifying the concept.

Many of the forms in Physics are defined in terms of a metric. For instance the work done by a particle against a force field uses the 1 form that is the inner product of a vector with the force field.

But the idea of integration over an oriented volume does not require a metric. Relying on Physics examples only can obscure this.

Last edited: Nov 6, 2014