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Peskin equation (6.46)

  1. Dec 21, 2011 #1
    I don't quite get the argument peskin used to obtain equation(6.46), page 191:
    [tex]\int{\frac{d^{4}l}{(2\pi)^4}\frac{l^{\mu}l^{\nu}}{D^3}}=\int{\frac{d^{4}l}{(2\pi)^4}\frac{\frac{1}{4}g^{\mu\nu}l^2}{D^3}}[/tex]
    He said"The integral vanishes by symmetry unless [itex]\mu=\nu[/itex]. Lorentz invariance therefore requires that we get something proportional to [itex]g^{\mu\nu}[/itex]......".
    I don't understand the "Lorentz invariance therefore....." part. How can one deduce from Lorentz invariance that LHS is an invariant tensor?
    I can convince myself the result by arguing spherical symmetry of the integrand, but I just want to understand Peskin's reasoning.
     
  2. jcsd
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