  As shown by Epstein and Glaser, the operator valued distribution (OPVD)
formalism permits to obtain a non-standard regularization scheme which leads to
a divergences-free quantum field theory. We show, with the example of a scalar
quantum electrodynamics theory, that Gaussian functions may be used as test
functions in this approach. After a short recall about the OPVD formalism in
3+1-dimensions, Gaussian functions and Harmonic Hermite-Gaussian functions are
used as test functions. The vacuum fluctuation, Feynman propagators and a study
about loop convergence with the example of the tadpole diagram are given. The
approach is extended to Quantum Electrodynamics. Calculations concerning
triangle anomaly and Ward-Takahashi identity are performed in the framework of
the method.
