# A formula for the photon gas correlation function

i need to derive a formula for the photon gas correlation function $\left\langle\partial n_i\partial n_j\right\rangle$ where $$\partial n_i=n_i -\left \langle n_i \right \rangle.$$

whilst solving I saw that $$\left \langle n_in_j \right \rangle = \frac{1}E. \frac{\partial ^2E}{\partial \beta \epsilon _i.\partial \beta \epsilon _j} =\frac{1}{E}\frac{\partial }{\partial (-\beta \epsilon _j)}(E\left \langle n_i \right \rangle)$$ but that says $\left \langle n_i \right \rangle\left \langle n_j \right \rangle i\neq j$ that means $n_i$ and $n_j$ are uncorrelated. I don't understand. How is this possible?

• yes i found it and i did understand it ... $\left \langle n_i \right \rangle$ $i=j$ since $\left \langle n_i^2 \right \rangle =\left \langle n_i \right \rangle$ therefore $g_i_j = \left \langle n_i \right \rangle \left \langle n_j \right \rangle (1-\partial _i_j)$ – relston mendonsa Jul 3 '14 at 21:43