  A generalized Feynman-Kac formula based on the Wiener measure is presented.
Within the setting of a quantum particle in an electromagnetic field it yields
the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup.
In this case rigorous criteria for its validity are compiled. Finally,
phase-space path-integral representations for more general quantum Hamiltonians
are derived. These representations rely on a generalized Lie-Trotter formula
which takes care of the operator-ordering multiplicity, but in general is not
related to a path measure.
