Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections

Sergio Albeverio ()
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Sergio Albeverio: University of Bonn, Institute for Applied Mathematics and Hausdorff Center for Mathematics

A chapter in When Form Becomes Substance, 2022, pp 267-282 from Springer

Abstract: Abstract Feynman path integrals are first presented for the case of non-relativistic quantum mechanics, both in physical and mathematical terms. Then the case of scalar relativistic and Euclidean quantum fields is discussed, with a particular consideration of the mathematical problems arising when discussing interactions as non-linear functionals of the fields. The methods of (constructive) perturbation theory and renormalization theory in relation to Feynman path integrals are briefly discussed, in particular mentioning the visual help provided by Feynman diagrams. The paper ends with mentioning some open problems and presenting some philosophical remarks and reflections on the description of natural phenomena, in particular those of fundamental physics, in mathematical terms.

Keywords: Quantum Feynman diagrams; Path integrals; Quantum field; Divergence; Renormalization (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-83125-7_9

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DOI: 10.1007/978-3-030-83125-7_9

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