  The first part of this thesis proposes a general approach to infinite
dimensional non-Gaussian analysis, including the Poissonian case. In particular
distribution theory is developed. Using appropriate integral transformations,
generalized and test functionals are characterized in terms of holomorphy.
Furthermore differential operators, Wick product and change of measure are
discussed.
  In the second part the Gaussian case (White Noise Analysis) is worked out in
more detail. Furthermore operators on distribution spaces e.g. compositions
with shifts and complex scaling are discussed.
  In the third part Feynman integrals are constructed using White Noise
distributions as integrands. Its expectation yields the path integral. This
rigorous approach is applied to the interacting case. A generalization of the
Khandekar Streit method is proposed. The resulting class of admissible
potentials covers signed measures. The Albeverio Hoegh-Krohn class, which
consists of Fourier transforms of measures, is discussed. The third approach is
based on complex scaling. The so-called Doss class allows analytic potentials
which obey some growth condition. Using the White Noise calculus of
differential operators, the functional form of the canonical commutation
relation is derived. Finally Ehrenfest's theorem is proven.
