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Fiber Structure and Stability Theorems for Symmetry Breaking Transitions
Version 1
: Received: 5 March 2024 / Approved: 5 March 2024 / Online: 6 March 2024 (10:15:05 CET)
How to cite: Bodnia, E. Fiber Structure and Stability Theorems for Symmetry Breaking Transitions. Preprints 2024, 2024030311. https://doi.org/10.20944/preprints202403.0311.v1 Bodnia, E. Fiber Structure and Stability Theorems for Symmetry Breaking Transitions. Preprints 2024, 2024030311. https://doi.org/10.20944/preprints202403.0311.v1
Abstract
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].
Keywords
Fiber bundle, phase transitions, Lie groups, homotopy,
fundamental group, Stability Theorem, Stability Lemma, Fiber Structure
Theorem, superfluid Helium
fundamental group, Stability Theorem, Stability Lemma, Fiber Structure
Theorem, superfluid Helium
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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