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

Grassman numbers and change of variables

  1. May 14, 2012 #1
    Quick question about Grassman numbers and change of variables.

    Suppose you have the function:

    [tex]f=\frac{c\epsilon_{ij} }{2!} \psi_i \psi_j[/tex]

    and integrate it:

    [tex]\int d\psi_2 d\psi_1 \frac{c\epsilon_{ij} }{2!} \psi_i \psi_j =c [/tex]

    Now change variables: [tex]\psi_i=J_{ik}\psi'_k [/tex] to get:

    [tex]\int d\psi_2 d\psi_1 \frac{c\epsilon_{ij} }{2!} \psi_i \psi_j=
    \int J_{2r} J_{1s}d\psi'_r d\psi'_s \frac{c\epsilon_{ij} }{2!} J_{im}\psi'_m J_{jn} \psi'_n
    \int det[J]d\psi'_2 d\psi'_1 \frac{c\epsilon_{mn} }{2!} det[J] \psi'_m \psi'_n
    =c [/tex]

    Doesn't this imply that det[J]2 has to equal one though? That can't be right.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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