# Peskin equation (6.46)

1. Dec 21, 2011

### kof9595995

I don't quite get the argument peskin used to obtain equation(6.46), page 191:
$$\int{\frac{d^{4}l}{(2\pi)^4}\frac{l^{\mu}l^{\nu}}{D^3}}=\int{\frac{d^{4}l}{(2\pi)^4}\frac{\frac{1}{4}g^{\mu\nu}l^2}{D^3}}$$
He said"The integral vanishes by symmetry unless $\mu=\nu$. Lorentz invariance therefore requires that we get something proportional to $g^{\mu\nu}$......".
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.