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The problem of renormalization in perturbative quantum field theory (pQFT)can be described in a rigorous way through the theory of extension ofdistributions. In the framework of pQFT a certain type of distribution appears,given by products of Green functions which act by integration with a testfunction. They present ultraviolet divergences, whenever any pair of argumentscoincide on one point of spacetime, and therefore, they are not definedeverywhere. In this work we have studied the necessary and sufficientconditions for the extension (or regularization) of this type of distribution.Moreover, we have constructed such extensions explicitly, satisfying a seriesof physically relevant axioms, such as the axiom of causality.

Quantum field theory and renormalization \`a la St\"uckelberg-Petermann-Epstein-Glaser