Spectral representation of hard thermal loops

In the theory of QCD at nonzero temperature, an important role is played by the leading terms at high temperature, which are of order T² (in the imaginary-time formalism). For the n-gluon function, implicit expressions are known for the T² terms, but they are in general singular for real values of the energies. Their analytic structure may be shown in the spectral representations written down by Evans. Here I display the Evans spectral function for the T² part of the n-gluon function for $n=2, 3, 4$. In each case there is only a single spectral function which is totally symmetric both in the n momenta and in the n Lorentz indices. I also state the Ward identities satisfied by the spectral functions.