Fiber Structure and Stability Theorems for Symmetry Breaking Transitions

Eve Bodnia

doi:10.20944/preprints202403.0311.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 5 March 2024 / Approved: 5 March 2024 / Online: 6 March 2024 (10:15:05 CET)

We discuss three key points: defining mathematically the notions of phase, symmetry breaking, topological defects and their stability in a formal language of homotopy theory and fiber bundle formalism; postulating and proving two theorems for successive symmetry breaking scenarios in condensed matter physics and cosmology, and demonstrating application of theorems to superfluid Helium 3 and Kibble-Lazarides-Shafi (KLS) walls, supporting and mathematically justifying the results of [Volovik, 2020].

Fiber bundle, phase transitions, Lie groups, homotopy,
fundamental group, Stability Theorem, Stability Lemma, Fiber Structure
Theorem, superfluid Helium

Physical Sciences, Mathematical Physics

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Fiber Structure and Stability Theorems for Symmetry Breaking Transitions

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