I don't quite get the argument peskin used to obtain equation(6.46), page 191:(adsbygoogle = window.adsbygoogle || []).push({});

[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.

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# Peskin equation (6.46)

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