IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-13678-8_7.html
   My bibliography  Save this book chapter

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

In: Logos and Alogon

Author

Listed:
  • Arkady Plotnitsky

    (Purdue University, Literature, Theory, and Cultural Studies Program, Philosophy and Literature Program)

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.

Suggested Citation

  • Arkady Plotnitsky, 2022. "Physics as Modern Mathematics: From Relativity to Quantum Theory, and Beyond," Springer Books, in: Logos and Alogon, chapter 0, pages 221-284, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13678-8_7
    DOI: 10.1007/978-3-031-13678-8_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-13678-8_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.