No coin nor oath required. For personal study only.
Previous work relating the thermodynamic potential to elementary particle S-matrix elements is generalized and re-derived directly from the expressions for the diagrams of many body theory. The divergent physical region poles are shown to introduce energy derivatives of mass shell delta functions which tend to shift the energies of the scattering particles away from the elementary particle mass shell. These shifted energies are related to the statistical quasi-particle energies introduced by Balian and De Dominicis. The work of these authors is generalized to show that to all orders in the coupling strengths the many body diagrams for any system described by a relativistic or non-relativistic field theory can be summed to give: (1) the entropy and the statistical average of a non-spontaneously broken, conserved charge in terms of ideal gas like formulae involving statistical quasi-particle energies; (2) the thermodynamic potential in terms of diagonal matrix elements of products of transition amplitudes wherein the energies of all external particles and the energy arguments of all ideal gas occupation numbers are the statistical quasi-particle energies.
๐ SIMILAR VOLUMES