I would like to evaluate the following integral:(adsbygoogle = window.adsbygoogle || []).push({});

##\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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Integration using delta function and step function

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Integration using delta | Date |
---|---|

A Difficult cosh integral using Leibniz rule? | May 6, 2017 |

I Find total charge (using double integration) | Apr 15, 2017 |

I Need a little push on this integral using trig substitution. | Mar 15, 2017 |

A Why can't I use contour integration for this integral? | Dec 16, 2016 |

I Integration by Parts without using u, v | Nov 30, 2016 |

**Physics Forums - The Fusion of Science and Community**