In the final chapter of his book "An Interpretive Introduction to Quantum Field Theory", Paul Teller writes about three interpretations of renormalization in quantum field theory. In particular, Teller denotes one of these approaches "Real-Infinities Renormalization," which eschews regularization and as such, he concludes, doesn't make much sense. However, Teller suggests the "Real-Infinities" approach could possibly be made rigorous using Conway/surreal numbers. The relevant section of Teller's book can be found on Google Books here: Teller, pg. 162.
My question is this: has anyone tried to formulate renormalization in quantum field theories without the use of regulators, in terms of Conway/surreal numbers as suggested by Teller?
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