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2 results

Gauge Theory and the Geometrisation of Physics

Gauge Theory and the Geometrisation of Physics
  • Henrique De Andrade Gomes
  • Published online:
    30 January 2025
    Print publication:
    30 January 2025
  • This Element is broadly about the geometrization of physics, but mostly it is about gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the Standard Model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question this Element aims to answer is: why is descriptive redundancy fruitful for physics? I will provide three inter-related answers to the question: ``Why gauge theory?'', that is: why introduce redundancies in our models of nature in the first place? The first is pragmatic, or methodological; the second is based on geometrical considerations, and the third is broadly relational.

  • POINT-FREE GEOMETRY, OVALS, AND HALF-PLANES

  • GIANGIACOMO GERLA, RAFAŁ GRUSZCZYŃSKI
  • Journal:
    The Review of Symbolic Logic / Volume 10 / Issue 2 / June 2017
    Published online by Cambridge University Press:
    23 January 2017, pp. 237-258
    Print publication:
    June 2017

  • In this paper we develop a point-free system of geometry based on the notions of region, parthood, and ovality, the last one being a region-based counterpart of the notion of convex set. In order to show that the system we propose is sufficient to reconstruct an affine geometry we make use of a theory of a Polish mathematician Aleksander Śniatycki from [15], in which the concept of half-plane is assumed as basic.