  The issue discussed is a thermodynamic version of the Bern-Kosower master
amplitude formula, which contains all necessary one-loop Feynman diagrams. It
is demonstrated how the master amplitude at finite values of temperature and
chemical potential can be formulated within the framework of the world-line
formalism. In particular we present an elegant method how to introduce a
chemical potential for a loop in the master formula. Various useful integral
formulae for the master amplitude are then obtained. The non-analytic property
of the master formula is also derived in the zero temperature limit with the
value of chemical potential kept finite.
