- 1,340

- 30

##\displaystyle{\int_{-\infty}^{\infty} dp^{0}\ \delta(p^{2}-m^{2})\ \theta(p^{0})}##

##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0})^{2}-\omega^{2}]\ \theta(p^{0})}##

##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0}+\omega)(p^{0}-\omega)]\ \theta(p^{0})}##

##\displaystyle{= \frac{1}{2\omega}\int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0}+\omega)+(p^{0}-\omega)]\ \theta(p^{0})}##

##\displaystyle{= \frac{1}{2\omega}\int_{-\infty}^{\infty} dp^{0}\ \delta(2p^{0})\theta(p^{0})}##

Have I made a mistake somewhere?

The answer is supposed to be ##\frac{1}{\omega}## but I'm not sure how to proceed next.