Uploaded July 2019 | Updated September 2026, 2 hours ago
One of the central alleged obstacles to the interpretation of perturbative quantum field theory is the presence of ultraviolet divergences in empirically adequate models. While the presence of ultraviolet divergences has been taken to be an inevitable consequence of representing realistic field interactions, I argue that they are in fact an artifact of the failure to correctly handle to distributional character of field operators in standard characterizations of quantum field theory. By appealing to techniques from causal perturbation theory, I show that when the multiplication of distributions is handled correctly, ultraviolet divergences are avoided and hence renormalization in the standard sense is not necessary. Moreover, this solution to the ultraviolet problem can be incorporated into axiomatic approaches to quantum field theory. This analysis shows that what differentiates perturbative and axiomatic field theory is not their treatment of arbitrarily short distances.
Foundations of Quantum Field Theory: 2019 Annual Philosophy of Physics Conference
June 12 - 14, 2019
Michael Miller, University of Toronto
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One of the central alleged obstacles to the interpretation of perturbative quantum field theory is the presence of ultraviolet divergences in empirically adequate models. While the presence of ultraviolet divergences has been taken to be an inevitable consequence of representing realistic field interactions, I argue that they are in fact an artifact of the failure to correctly handle to distributional character of field operators in standard characterizations of quantum field theory. By appealing to techniques from causal perturbation theory, I show that when the multiplication of distributions is handled correctly, ultraviolet divergences are avoided and hence renormalization in the standard sense is not necessary. Moreover, this solution to the ultraviolet problem can be incorporated into axiomatic approaches to quantum field theory. This analysis shows that what differentiates perturbative and axiomatic field theory is not their treatment of arbitrarily short distances.
Foundations of Quantum Field Theory: 2019 Annual Philosophy of Physics Conference
June 12 - 14, 2019
Michael Miller, University of Toronto
Visit the Rotman website for more information on applications, events, project descriptions, and openings. rotman.uwo.ca
Follow The Rotman Institute on Twitter: twitter.com/rotmanphilo
Like The Rotman Institute on Facebook: facebook.com/rotmanphilosophy
Subscribe to our channel: youtube.com/user/rotmanphilosophy
