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

Diffeomorphisms to poincare

  1. Oct 12, 2011 #1
    Hi,

    I'm sorry to have to ask this, but I can't seem to reason this one out by myself at the moment. Given the metric is the Minkowski spacetime, is the group of diffeomorphisms the poincare group, or are there diffeomorphisms for flat-space that are not metric preserving?

    I would really appreciate your help. Thanks,

    EDIT: Nevermind, sorry for making a new thread for this... I had some tea and thought it out.
     
    Last edited: Oct 12, 2011
  2. jcsd
  3. Oct 12, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    So you reached the conclusion that there are diffeomorphisms which are not isometries ?
     
  4. Oct 12, 2011 #3
    yes. there are definitely diffeomorphisms that are not isometries, a lot of them even for the minkowski metric.
     
  5. Oct 12, 2011 #4

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    Yeah, remember that passive diffeomorphisms are just coordinate changes, and I'm sure you can imagine all kinds of coordinates on Minkowski space that have nothing to do with isometries.
     
  6. Oct 12, 2011 #5
    A diffeomorphism is just a (smooth, invertible) map from the manifold to itself. No need to even have a metric to talk about diffeomorphisms.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Diffeomorphisms to poincare
  1. Poincare transform (Replies: 7)

  2. Active diffeomorphism (Replies: 13)

  3. Poincare' group (Replies: 5)

Loading...