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

What is the physical significance of Poisson brackets?

  1. May 12, 2015 #1
    I know the definition of the Poisson bracket and how to derive elementary results from it, but I'm struggling to understand intuitively what they are describing physically? For example, the Poisson bracket between position [itex]q_{i}[/itex] and momentum coordinates [itex]p_{j}[/itex] is given by [tex]\lbrace q_{i},p_{j}\rbrace = \delta_{ij}[/tex]
    but what is this describing physically? is it that momentum generates a change in position or is it something else?

    Also, how is the Poisson bracket motivated? Is it a quantity that arises naturally which we define to be the Poisson bracket, or is it derived in some manner?
     
  2. jcsd
  3. May 12, 2015 #2

    jedishrfu

    Staff: Mentor

  4. May 12, 2015 #3
    Thanks for the link. I've actually already had a look at that thread and it didn't really help unfortunately.

    I think part of the issue is how to interpret the fact that the Poisson bracket for position and momentum is non-zero, but these commute in classical mechanics (the confusion arising from the fact that people often seem to describe the Poisson bracket by comparing it to the quantum commutator)?!
     
  5. May 12, 2015 #4

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    This might help...
    (it's been on my to-read list)
    http://projecteuclid.org/euclid.cmp/1103907394
    On the relation between classical and quantum observables (Abhay Ashtekar)

    There's a geometrical interpretation involving the symplectic form in phase space... but I haven't absorbed it well enough to explain.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is the physical significance of Poisson brackets?
  1. About Poisson brackets (Replies: 6)

  2. Poisson brackets (Replies: 5)

Loading...