1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kaku, Quantum Field Theory Page 47 (2.68/9)

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Here is equation (2.68)
    [tex](M^{ij})_{ab} = -i(\delta^i_a\delta^j_b - \delta^j_a\delta^i_b)[/tex]

    Here is equation (2.69) (abbreviated)
    [tex][M^{ij},M^{lm}]_{ab} = +i\delta^{jl}(M^{im})_{ab} +- ...[/tex]

    The problem is to show that (2.68) implies (2.69)

    2. Relevant equations

    3. The attempt at a solution
    [tex][M^{ij},M^{lm}]_{ab} = (M^{ij})_{ac}(M^{lm})_{cb} - (M^{lm})_{ac}(M^{ij})_{cb}[/tex]
    [tex]= -(\delta^i_a \delta^j_c - \delta^j_a \delta^i_c)(\delta^l_c \delta^m_b - \delta^m_c \delta^l_b) + (\delta^l_a \delta^m_c - \delta^m_a \delta^l_c)(\delta^i_c \delta^j_b - \delta^j_c \delta^i_b)[/tex]
    [tex]= -\delta^i_a\delta^{jl}\delta^m_b + \delta^m_a\delta^{jl}\delta^i_b +- ...[/tex]
    [tex]= -i\delta^{jl}(M^{im})_{ab} +- ...[/tex]

    This is (2.69) times a factor of -1. Am I wrong, or is Kaku. If Kaku, then what it correct. I have tried to find this equation in other books, but without success. I was able to confirm equation (2.88) on page 51 using equation (2.87). Note the leading minus sign on the right hand side of (2.68) which is not found on (2.87).
  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: Kaku, Quantum Field Theory Page 47 (2.68/9)
  1. Quantum Field Theory (Replies: 5)

  2. Quantum Field Theory (Replies: 42)

  3. Quantum Field Theory (Replies: 3)

  4. Quantum Field Theory (Replies: 3)