Useful model to understand Schwartz’ distributions’ approach to non-renormalizable QFTs

Useful model to understand Schwartz’ distributions’ approach to non-renormalizable QFTs

Quantum Field Theory (QFT) is a difficult subject, plagued by puzzling infinities. Its most formidable challenge is the existence of many non-renormalizable QFT theories, for which the number of infinities is itself infinite. We will here appeal to a rather non-conventional QFT approach developed in...

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Veröffentlicht in:Brazilian journal of physics 2021-06, Vol.51 (3), p.803-812
Hauptverfasser: Rocca, M. C., Plastino, A.
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Field theory
Particles and Fields
Physics
Physics and Astronomy
Quantum field theory
Quantum theory
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description Quantum Field Theory (QFT) is a difficult subject, plagued by puzzling infinities. Its most formidable challenge is the existence of many non-renormalizable QFT theories, for which the number of infinities is itself infinite. We will here appeal to a rather non-conventional QFT approach developed in [J. of Phys. Comm. 2 115029 (2018)] that uses Schwartz’ distribution theory (SDT). This technique avoids the need for counterterms. In the SDT approach to QFT, infinities arise due to the presence of products of distributions with coincident point singularities. In the present study, we will carefully discuss a simple QFT-model devised by Bollini and Giambiagi. Because of its simplicity, it makes easy to appreciate just how it is possible to successfully deal with the issue of non-renormalizability via SDT.
doi_str_mv 10.1007/s13538-021-00882-y
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subjects Field theory
Particles and Fields
Physics
Physics and Astronomy
Quantum field theory
Quantum theory
title Useful model to understand Schwartz’ distributions’ approach to non-renormalizable QFTs
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