Return to Answer

The answer to your question depends on whether you are interested in the perturbative RG or the nonperturbative one.

Dec 2017 edit: I just put a hopefully useful detailed complement to this post on https://physics.stackexchange.com/questions/372306/wilsonian-definition-of-renormalizability

The answer to your question depends on whether you are interested in the perturbative RG or the nonperturbative one.

Update: A short pedagogical presentation, elaborating on the above answer can be found here. The slides of my recent talk "A Toy Model for Three-Dimensional Conformal Probability" also provides more details on how the renormalization group allows one to construct QFTs as weak limits of cut-off probability measures on spaces of Schwartz distributions, for the simplest example that contains the germs of generality. The precise formulation of the problem of constructing a QFT to be solved by renormalization group techniques can be found in my answer to this MO question.

Update: A short pedagogical presentation, elaborating on the above answer can be found here. The slides of my recent talk "A Toy Model for Three-Dimensional Conformal Probability" also provides more details on how the renormalization group allows one to construct QFTs as weak limits of cut-off probability measures on spaces of Schwartz distributions, for the simplest example that contains the germs of generality. The precise formulation of the problem of constructing a QFT to be solved by renormalization group techniques can be found in my answer to this MO question.

Update: A short pedagogical presentation, elaborating on the above answer can be found here. The slides of my recent talk "Vers une théorie probabiliste des champs conformes en dimension trois" also provides more details on how the renormalization group allows one to construct QFTs as weak limits of cut-off probability measures on spaces of Schwartz distributions, for the simplest example that contains the germs of generality.

Update: A short pedagogical presentation, elaborating on the above answer can be found here. The slides of my recent talk "A Toy Model for Three-Dimensional Conformal Probability" also provides more details on how the renormalization group allows one to construct QFTs as weak limits of cut-off probability measures on spaces of Schwartz distributions, for the simplest example that contains the germs of generality. The precise formulation of the problem of constructing a QFT to be solved by renormalization group techniques can be found in my answer to this MO question.