Physics as Modern Mathematics: From Relativity to Quantum Theory, and Beyond

Arkady Plotnitsky
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Arkady Plotnitsky: Purdue University, Literature, Theory, and Cultural Studies Program, Philosophy and Literature Program

Chapter Chapter 7 in Logos and Alogon, 2022, pp 221-284 from Springer

Abstract: Abstract This chapter addresses two key aspects of the relationships between modern mathematics and physics, relationships that developed even though the project of modern mathematics was shaped by its aim of separating itself from physics. The first is the ability of physics, especially relativity and quantum theory, to use the concepts and theories of modern mathematics born from this separation. The second is the influence that theoretical physics has exerted on algebra, functional analysis, differential geometry, algebraic topology, and algebraic geometry, in sum on all key areas of modern mathematics. After a brief introduction, Sect. 7.2 considers the use of modern mathematics in relativity and quantum theory. Section 7.3 discusses the Pythagorean and radically Pythagorean character of quantum theory, in (reality-without-realism) RWR-type interpretations. Section 7.4 considers the transformation of the concept of elementary particles in quantum field theory. Section 7.5 is devoted to the role of symmetry and group representation in quantum theory. Finally, Sect. 7.6 addresses with a sharper focus (as the subject is discussed in earlier sections as well) the influence of physics on mathematics, by considering, as an example, the impact of the Yang-Mills theory, which grounds the standard model of elementary particle physics, on differential topology.

Keywords: Galois theory; Group representations; Quantum field theory; Quantum mechanics; Relativity; Yang-Mills theory (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-031-13678-8_7

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