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Why are there ultraviolet divergences at all?While the presence of ultraviolet divergences has been taken to be an inevitable consequence of representing realistic field interactions, by appealing to techniques from causal perturbation theory I argue that they are in fact an artifact of the particular choice of mathematical
structures that are used in standard characterizations of quantum field theory. I show that with a different choice of structures the divergences, and hence renormalization, can be avoided. I argue that this situation motivates taking formal power series seriously as the mathematical objects to which physical meaning accrues in empirically adequate models.
Department of History and Philosophy of Science
University of Pittsburgh