  Given the real Clifford algebra of a quadratic space with a given signature,
we define a new product in this structure such that it simulates the Clifford
product of a quadratic space with another signature different from the original
one. Among the possible applications of this new product, we use it in order to
write the minkowskian Dirac equation over the euclidean spacetime and to define
a new duality operation in terms of which one can find self-dual and
anti-self-dual solutions of gauge fields over Minkowski spacetime analogous to
the ones over Euclidean spacetime and without needing to complexify the
original real algebra.
