Circular symmetry-breaking and topological Noether currents

TL;DR

This paper introduces a toy model linking circular symmetry-breaking to topological phenomena, interpreting Planck's radiation law as a symmetry loss during bubble collapse, with implications for algebraic topology and physics.

Contribution

It presents a novel algebraic topology framework for bubbling as symmetry-breaking, connecting Noether currents, cobordism, and physical phenomena like radiation laws.

Findings

Interpretation of Planck's law via symmetry loss during bubble collapse

Development of a toy model for algebraic topology of bubbling

Connection between cobordism of manifolds with circle actions and physical processes

Abstract

We propose a toy model for the algebraic topology of bubbling as circular symmetry-breaking, in terms of asymptotic expressions for Noether currents and cobordism of manifolds with circle actions free along boundaries. This leads to an interpretation of Planck's radiation law as the loss of a Noether symmetry when a bubble $[S^2/\mathbb{T}] \to {\rm pt}$ (analogous to blowing up or down in projective geometry) collapses, much like the von K\'arm\'an street of sparks left when a candle flame wisps out.