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

Feynman-Kac formula

  1. Apr 30, 2012 #1
    Hi,

    can anyone explain to me, how the Feynman-Kac formula is used to obtain the following expression for the N-particle canonical partition function of a Bose gas (with interaction potential V)?

    Z=1/N!Ʃ_{π\in S_N}Ʃ_{x1,...,xn}E[ exp(-∫_0^β Ʃ_{i<j}V(X_i(s), X_j(s) ds*indicator(X_i(β)=xπ(i), i=1...N) ]

    where X_i(t) are independent continuous time simple symmetric random walks, X_i(0)=x_i.

    As far as I know, the Feynman-Kac formula is a tool for solving parabolic differential equations, and I just don't know why the above is true.

    Thank you for your help!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Feynman-Kac formula
  1. Feynman Paths (Replies: 6)

  2. Feynman diagram (Replies: 2)

  3. Feynman on reflection (Replies: 3)

  4. Feynman Diagrams (Replies: 2)

  5. Feynman rules (Replies: 0)

Loading...