Is Dirac's Delta to the fourth power equal to 0.5?

[zn5252]

hello,
Please attached snapshot. Does the integral 7.9 equal to 0.5 $\int$h_μσ dz^μ/dτ dz^σ/dτdτ ?
I'm confused as to the fourth power of Dirac's Delta. Then where does the derivative on x go ?
For more on this, see MTW pg180
thanks

 

[Bill_K]

It's not a 4th power, it means a four-dimensional delta function. I.e. in Minkowski coordinates,

δ⁴(x - x') = δ(x - x')δ(y - y')δ(z - z')δ(t - t')

Ofttimes you would integrate this over all four dimensions. In this case there is only one integration, leaving three δ's, so it means that T^μν(x) is concentrated on the particle's worldline.