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

Fourier transform of integration measure (Peskin and Schroeder)

  1. Apr 3, 2013 #1
    At page 285 in Peskin and Schroeder's Introduction to quantum field theory the author defines the integration measure [itex]D\phi = \Pi_i d\phi(x_i)[/itex] where space-time is being discretised into a square lattice of volume L^4. He proceeds by Fourier-transforming

    [tex] \phi(k_n) = \frac{1}{V} \sum_n e^{-i k_n \cdot x_i} \phi(k_n)[/tex]

    and considering only [itex]k^0_n >0[/itex] as independent variables he concludes that since the fourier transformation is unitary, the measure [itex]D\phi = \Pi_i d\phi(x_i)[/itex] can equivalently be expressed as (equation 9.22)

    [tex] D\phi = \Pi_{k_n^0 > 0} d Re \phi(k_n) d Im \phi(k_n).[/tex]

    Why is he only considering [itex]k^0_n >0[/itex] and how does he arrive at this conclusion? What is the relevance of the fourier transform being unitary?
     
  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: Fourier transform of integration measure (Peskin and Schroeder)
  1. Peskin, Schroeder (Replies: 8)

Loading...