(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

let be [tex] A_{i,j} [/tex] a Hermitian Matrix with only real values then

[tex] \int_{V} dV e^{iA_{j,k}x^{j}x^{k}}= \delta (DetA) (2\pi)^{n} [/tex] (1)

2. Relevant equations

[tex] \int_{V} dV e^{iA_{j,k}x^{j}x^{k}} = \delta (DetA) (2\pi)^{n} [/tex]

3. The attempt at a solution

the idea is that the integral (1) is divergent when the Matrix A is not invertible Det=A and the Dirac delta is not defined at x=0 ,for example if detA=0 then at least one of the eigenvalues is 0 so the exponential takes the value 1 and the integral is divergent

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Homework Help: Integral of a complex exponential

**Physics Forums | Science Articles, Homework Help, Discussion**