Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,354 answers , 22,791 comments
1,470 users with positive rep
820 active unimported users
More ...

  What phenomena in physics cannot be expressed in terms of differential forms?

+ 0 like - 0 dislike
747 views

It seems all phenomena in physics can be expressed in terms of differential forms. There are textbooks dedicated to formulating the main theories of physics in terms of differential forms. The more general formulation in terms of Tensors however I think is more often used by physicists. Differential forms seem to carry much advantage in terms of unification, simplicity in higher dimensional theories and generalization. Considering that a differential form is just an antisymmetric covariant tensor on a differential manifold (i.e a specialized form of tensor), what phenomena in physics cannot be re-formulated in the notation of differential forms or can we always reformulate our laws in this notation? If we can reformulate in terms of differential forms, why would we choose not to?

asked Jun 29, 2020 in Theoretical Physics by Kay Bei (10 points) [ no revision ]

1 Answer

+ 1 like - 0 dislike

Regarding "If we can reformulate in terms of differential forms, why would we choose not to?" let me ask "Suppose we could reformulate, why should we?". Because some books/physicists firmly advocate the differential form approach? In my opinion certainly not. Physicists are not automatons but individuals with personal tastes and preferences, which to hold they are perfectly entitled.

Considering the various formulations available it should always be kept in mind that the physics behind the formulations is the same. Depending on the specific problem at hand, one or the other of the formulations may be more advantageous.

In Hamilton dynamics, differential forms allow a concise formulation of canoncial transformations or constraints, but can also be largely avoided by using Poisson brackets. In case of specific calculations, i.e. where you have to deal with numbers, you will end up working with some kind of components (e.g. coefficients for a basis of 1-forms or coordinates) anyway.

In electrodynamics, you can for example write down the theory in terms of differential forms, or in relativistic index notation, or in three-dimensional vector notation. The physics is the same. If you are considering a problem in electrostatics, which formulation would you prefer?

There is only one physics, but various formulations. The more formulations you are familiar with, the larger the set of tools you can choose from when addressing a problem.

Not all tensors in physics are antisymmetric. There is the metric tensor, which can be written with 1-forms \(g=g_{ab}dx^a\otimes dx^b\), but which is not a 2-form, or the energy-momentum tensor. Then there are also concepts like spinors.

So there is one physics, but not The One And Only Way of expressing it.

answered Jun 29, 2020 by Flamma (110 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOve$\varnothing$flow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...