Symmetry of Bounce Solutions at Finite Temperature

2025/11/08 by Shoji, Yutaro, Yamaguchi, Masahide · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2511.05950

openalex publication_date 2025/11/08 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

The seminal work of Coleman, Glaser, and Martin established that, at zero temperature, any non-trivial solution to the equations of motion with the least Euclidean action is O(D)-symmetric. This paper extends their foundational analysis to finite temperature. We rigorously prove that for a broad class of scalar potentials, any saddle-point configuration with the least action is necessarily O(D - 1)-symmetric and monotonic in the spatial directions. This result provides a firm mathematical justification for the symmetry properties widely assumed in studies of thermal vacuum decay and cosmological phase transitions.

Citations

• On the Metastability of Quantum Fields in Thermal Bath
• Is the Coleman de Luccia action minimum?: AdS/CFT approach
• Symmetry and monotonicity of least energy solutions
• Comments on Nonlinear Wave Equations as Models for Elementary Particles

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