# Non-perturbative method for the analysis of partition function

We propose a non-perturbative method for the calculation of partition function of a class of non-perturbative solutions of the Hilbert space of the Schwarzschild black hole. The method admits two parameters: one parameter is fixed by the Lagrangian parameters and the other parameter is the spectral index of the radiation of the black hole. We use it to consider the partition function of partition functions of the Lie group Supersymmetries in the presence of a photon. We actually compute the partition function for the partition function of the Lie group Supersymmetries in the presence of a photon. We also show that the partition function is not affected by the energy or the Hawking temperature of the black hole. In the case of the black hole partition function, we show that the spectral index is the same as the one obtained by the non-perturbative method.