What are the general conditions for a scalar field theory to be renormalizable? What additional conditions arise for spin-1/2 and spin-1(if any)?
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One short definition is that if a theory is renormalizable, then the adjustment of a finite number of parameters (such as the bare electron charge and mass) allows us to calculate the results of all observable in finite terms.
My question, as part of this short answer to the OP, (and which I lack the knowledge to answer) is:
Based on the extract below: Are we satisfied today that Feymans reservations (as just one example) about renormalization are deemed out of date?
Or is the process still slightly in the realm of quantum interpretations, in that, without being blase or glib, we can say: it works, we would like to know more about it as much as we would like know more about the real nature of a photon or the "size" of an electron, but mainly we are happy that it works.
The renormalization group as developed along Wilson's breakthrough insights relates effective field theories at a given scale to such at contiguous scales. It thus describes how renormalizable theories emerge as the long distance low-energy effective field theory for any given high-energy theory. As a consequence, renormalizable theories are insensitive to the precise nature of the underlying high-energy short-distance phenomena (the macroscopic physics is dominated by only a few "relevant" observables). This is a blessing in practical terms, because it allows physicists to formulate low energy theories without detailed knowledge of high-energy phenomena. It is also a curse, because once a renormalizable theory such as the standard model is found to work, it provides very few clues to higher-energy processes.
I have just found a duplicate here Semantic Problem about Renormalization but I am not sure if it is at the level the OP is looking for (no offence, it's certaintly beyond me)
