  This is the first paper in a series that deals with solar-physics
applications of the equation-of-state formalism based on the formulation of the
so-called "Feynman-Kac (FK) representation". Here, the FK equation of state is
presented and adapted for solar applications. Its domain of validity is
assessed. The practical application to the Sun will be dealt with in Paper II.
Paper III will extend the current FK formalism to a higher order. Use of the FK
equation of state is limited to physical conditions for which more than 90% of
helium is ionized. This incudes the inner region of the Sun out to about .98 of
the solar radius. Despite this limitation, in the parts of the Sun where it is
applicable, the FK equation of state has the power to be more accurate than the
equations of state currently used in solar modeling. The FK approach is
especially suited to study physical effects such as Coulomb screening, bound
states, the onset of recombination of fully ionized species, as well as
diffraction and exchange effects. The localizing power of helioseismology
allows a test of the FK equation of state. Such a test will be beneficial both
for better solar models and for tighter solar constraints of the equation of
state.
