# MTW definition of differential froms made rigorous

• micromass
In summary, the conversation discusses the topic of differential forms and the speaker's struggle to understand the formal theory and connect it to a more intuitive understanding. They share a paper that offers a helpful perspective and ask for further resources or theorems that can bridge the gap between the two. The conversation also mentions the speaker's personal project and shares a conference poster with relevant references. The conversation ends with a thank you to one of the participants for their helpful input.
micromass
Staff Emeritus
Homework Helper
Hello guys!

I've been trying to get some intuition for differential forms. I know the formal theory and I know how useful they are. But then I came across the following paper: https://dl.dropboxusercontent.com/u/828035/Mathematics/forms.pdf
It describes an intuition for forms that is very closely related to how forms are described in MTW. It's really nice.

The only problem is that I have no clue how to make this rigorous. So does anybody know some theorems or results that connect the intuitive picture as described in the pdf to the formal theory of forms. In particular, given a ##1##-form (or an ##n##-form more generally), how does one draw the associated picture in the pdf?

Thanks a lot!

I've been working on a way to draw these accurately in 3-D using VRML, Maple, and VPython...
but that's been on the backburner due to different but related projects.

Here is an old conference poster of mine (on an old website of mine [I'm no longer there]).
Have a look at the references listed.

Last edited by a moderator:
2 people
Thanks a lot robphy. The references to your conference poster were really helpful. The two books by Burke and Sternberg give really good intuition and explained a lot to me. I think I have finally figured out how to make the pdf in my OP rigorous with the help of your post.

## 1. What is the MTW definition of differential forms?

The MTW definition of differential forms is a mathematical concept used in differential geometry and differential topology. It defines a differential form as a type of geometric quantity that can be integrated over a manifold, allowing for the calculation of various mathematical quantities such as flux and work.

## 2. How is the MTW definition of differential forms different from other definitions?

The MTW definition is different from other definitions in that it emphasizes the geometric nature of differential forms and their relationship to integrals on manifolds. It also provides a rigorous mathematical foundation for understanding differential forms, making them applicable to a wide range of mathematical problems.

## 3. Why is the MTW definition of differential forms important?

The MTW definition is important because it allows for a deeper understanding of differential forms and their applications in mathematics, physics, and other fields. It provides a rigorous framework for studying these objects and allows for the development of powerful mathematical tools.

## 4. What are some applications of the MTW definition of differential forms?

The MTW definition of differential forms has numerous applications in mathematics and physics, including in the study of vector calculus, differential geometry, and general relativity. It is also used in engineering, computer science, and other fields where the manipulation of geometric quantities is important.

## 5. Are there any limitations to the MTW definition of differential forms?

Like any mathematical definition, the MTW definition of differential forms has its limitations. It may not be applicable in certain situations or may not fully capture the complexity of a problem. It also requires a strong understanding of mathematical concepts, making it less accessible to those without a solid background in mathematics.

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