How Can I Improve My Understanding of Twisted Forms in Mathematics?

[bmegun]

Can anyone suggest insight, or a course of study, that can improve understanding of twisted (or pseudo) forms. I have learned from reading Frankel and Burke, that half the forms used in physical theory are twisted, and though I've studied their chapters on the subject, my intuition is still inadequate. It seems so strange to have developed an elaborate theory of intrinsic geometric objects (forms) and to then introduce a vestige of a coordinate system, by introducing orientation. Though Burke indicates that neither twisted or ordinary forms are more fundamental, I have not seen an intrisic definition of twisted forms. In any case, I would like to improve
my understanding and intuition, through simple examples, and or a reading
list.

 

[robphy]

I have also been trying to develop my intuition about twisted forms.

Have you already seen
(Burke) Twisted Forms as they should be ?

Here is a list of some references that may be helpful.
physics.syr.edu/courses/vrml/electromagnetism/references.html[/URL]

Additionally, http://www.icm.edu.pl/edukacja/mat/Compendium.php may be useful.

 

[M98Ranger]

One possible approach to improving your understanding of twisted forms could be to explore the mathematical concept of differential forms. Differential forms are a powerful tool for understanding and manipulating geometric objects, and they have applications in many areas of mathematics, including physics. They also provide a rigorous framework for understanding twisted forms.

Some recommended resources for studying differential forms include the book "Differential Forms in Algebraic Topology" by Raoul Bott and Loring Tu, as well as the online lecture notes "Differential Forms for Mathematicians" by Robert Bryant. These resources provide a thorough and intuitive introduction to the concept of differential forms and their applications.

In addition, studying differential geometry and topology can also help improve your understanding of twisted forms. These fields deal with the intrinsic geometry of spaces and provide a deeper understanding of the relationship between forms and coordinate systems.

Finally, it may also be helpful to work through examples and practice problems to gain a better intuition for twisted forms. Some possible resources for this include textbooks on differential geometry and topology, as well as online resources such as MathSE or MathOverflow.

Overall, improving your understanding of twisted forms will require a combination of studying theory, working through examples, and practicing problem-solving. With dedication and persistence, you can develop a deeper understanding and intuition for this important concept in mathematics and physics.