Symmetric Dual Breather Modes as a Dynamic Origin of Tiny Particle Masses
Abstract
Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes Z2 symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the "symmetric dual breather mode," whose phase-space geometry is traced using a t-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit (A ≪ ϕv1). As the amplitude increases into the heteroclinic regime (A > ϕv1), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter (⟨ ϕ⟩ = 0) and driving a geometric curvature cancellation (⟨ V''(ϕ) ⟩t → 0). Governed by a universal scaling function F(y), the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.
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BibTeX
@misc{iwata2026symmetric,
title = {{Symmetric Dual Breather Modes as a Dynamic Origin of Tiny Particle Masses}},
author = {Yoritaka Iwata and Yasuhiro Takei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15990},
eprint = {2610.15990},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15990},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetric Dual Breather Modes as a Dynamic Origin of Tiny Particle Masses
AU - Yoritaka Iwata
AU - Yasuhiro Takei
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15990
UR - https://arxiv.org/abs/2610.15990
AB - Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes Z_2 symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the "symmetric dual breather mode," whose phase-space geometry is traced using a t-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit (A ≪ ϕ_v1). As the amplitude increases into the heteroclinic regime (A > ϕ_v1), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter (⟨ ϕ⟩ = 0) and driving a geometric curvature cancellation (⟨ V''(ϕ) ⟩_t → 0). Governed by a universal scaling function F(y), the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.
ER -