TL;DR
This paper reflects on Gunnar Källén's work on infinities in quantum field theory, discusses the current status of the problem, and offers personal insights on potential future resolutions.
Contribution
It provides a historical and personal perspective on the infinities problem in quantum field theory and discusses possible future solutions.
Findings
Infinities pose fundamental challenges in quantum field theory.
Current approaches have not fully resolved the infinities issue.
Future developments may lead to a resolution of the infinities problem.
Abstract
This is the written version of a talk given in memory of Gunnar K\"{a}ll\'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of Gunnar K\"{a}ll\'{e}n, edited by C. Jarlskog and A. C. T. Wu. I discuss some of K\"{a}ll\'{e}n's work, especially regarding the problem of infinities in quantum field theory, and recount my own interactions with him. In addition, I describe for non-specialists the current status of the problem, and present my personal view on how it may be resolved in the future.
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Taxonomy
TopicsQuantum Mechanics and Applications · Advanced Thermodynamics and Statistical Mechanics