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Integrate over Dirac Deltas - avoid apparently odd behaviour?

GROUPS:

Take the following integration over Dirac delta functions

Integrate[DiracDelta[-k2 + p2]*DiracDelta[-k3 + q1]*DiracDelta[k4 + p1 - p2 + q1], 
  {p2, -Infinity, Infinity}, Assumptions -> Element[k2, Reals], 
  Assumptions -> Element[k4 + p1 + q1, Reals]]

which results in

DiracDelta[-k3 + q1]*DiracDelta[-k2 + k4 + p1 + q1]

However, if you try the following, with exactly the same set of Dirac delta function, combined with just plain functions, there is no result

Integrate[C[p1]*C[p2]*C[-p1 + p2 - q1]*C[q1]*DiracDelta[-k2 + p2]*
   DiracDelta[-k3 + q1]*DiracDelta[k4 + p1 - p2 + q1]*F1[p1, k1], 
  {p2, -Infinity, Infinity}, Assumptions -> Element[k2, Reals], 
  Assumptions -> Element[k4 + p1 + q1, Reals]]

Any suggestions on why Mathematica refuses to carry out the integration in the second case?

POSTED BY: Arny Toynbee
Answer
17 days ago

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