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# Product of Dirac deltas watch

1. In one of my classes yesterday, we equated the two quantities below and I am not sure why this holds. I queried the lecturer and she explained using convolution products, but I didn't really understand - I've only met them very briefly when playing with Fourier transforms.

Basically, I'm not sure how we've got rid of both delta functions (albeit both in ) but only integrated once. Any help appreciated

Thanks
2. (Original post by Implication)
In one of my classes yesterday, we equated the two quantities below and I am not sure why this holds. I queried the lecturer and she explained using convolution products, but I didn't really understand - I've only met them very briefly when playing with Fourier transforms.

Basically, I'm not sure how we've got rid of both delta functions (albeit both in ) but only integrated once. Any help appreciated

Thanks
I must admit, this looks a little odd. I would expect the answer to be

as it looks like the original integral is a convolution of delta functions and should therefore result in a single delta function. Unless someone here more knowledgeable about this stuff (Feynman diagrams?) comes along, it might be an idea to ask your lecturer again. Just a final thought...what happens next? What is this formula used for? You might find a clue in what it is plugged into!

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Updated: November 7, 2015
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