TL;DR
This paper explores how analogies have historically influenced theoretical physics, focusing on spontaneous symmetry breaking and the renormalization group, highlighting their roles in advancing physical theories.
Contribution
It provides an analysis of two complex cases demonstrating the nuanced ways analogies facilitate conceptual and mathematical development in physics.
Findings
Analogies link physical concepts with mathematical formalism.
Spontaneous symmetry breaking was introduced through analogy with phase transitions.
Renormalization group methods offer a statistical interpretation of critical phenomena.
Abstract
Analogies have had and continue to have an important role in the development of theoretical physics. They may start from similarities of physical concepts followed by similarities in the mathematical formalization or it may be a purely mathematical aspect to suggest the development of analogous physical concepts. More often a subtle non obvious interplay between these levels is involved. In this paper I will discuss two cases sufficiently intricate to illustrate some ways of how analogies work. The first topic is the introduction of spontaneous symmetry breaking in particle physics. The second one is the use of the renormalization group in the theory of critical phenomena and its statistical interpretation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.