Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Momentum and cotangent space

  1. Mar 18, 2003 #1


    User Avatar
    Gold Member

    We are told sometimes that (x,p) is to be considered a point in cotangent space T^*Q. The naivest argument for this is that momentum is a covector, so its transformation law under coordinate changes is just the transformation law of elements in the cotangent space. But for the same token force is a covector, so we also could said that Force lives in T^*Q.

    Worse, T^*Q is the dual to TQ, where vector fields live, and in this sense it is compossed of *differential* forms. So it seems that we should see momentum as coordinates of a differential form. But should we?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?