EIGENVALUES OF ENERGY LEVELS AND NONLINEAR INTERACTIONS FOR MULTIPARTICLE SYSTEM

The energy levels, En. of pions in multiparticle systems have been calculated by using the probability distribution, P(n,k), of the independent-creation model of multi-fire balls and the density matrix method of quantum statistics. The result, E_n = E₀ +nk_BTln( 1+1/n )-k_BTln x Γ(n+k) /Γ(k) Γ(n+1), shows that the nonlinear interaction depends on k. and it can take place only between different fire-balls.