Phase Encoding of Genuine Three-Body Interactions in a Relativistic Dirac System in 1+1 Dimensions
Abstract
We show how genuine three-body phase information can enter the invariant mass of a relativistic three-particle Dirac system in (1+1) dimensions. As a solvable reference system, we consider the Sakamoto--Munakata--Ino model with pairwise contact interactions gij(1−αiαj)δ(xi−xj). These singular interactions can be transferred into sector-dependent phases and matching conditions by a discontinuous unitary transformation. Although the explicit contact terms are thereby removed, the nonzero constituent-mass operator is rotated and retains nontrivial spectral information. We introduce a genuine three-body holonomy generated by Q3=α1α2α3. The kinetic and pair-interaction parts commute with Q3, while the constituent-mass operator anticommutes with it. Consequently, the massless system separates into the Q3=±1 sectors, which acquire opposite holonomy phases e± iθ3, whereas nonzero constituent masses mix the two sectors. This phase-sector-mixing mechanism makes the relative three-body phase dynamically accessible to the bound-state spectrum and establishes an operator-level mechanism through which the three-body holonomy generates a θ3 dependence of the physical three-body invariant mass. We further emphasize that the topological three-body holonomy is not automatically equivalent to a bare triple-contact potential; such an equivalence requires a regulated self-adjoint realization and a compatible interaction-dependent boost satisfying the Poincaré algebra. The resulting framework therefore connects genuine three-body phase information to the mass spectrum of a relativistic composite system while clearly separating the controlled holonomy construction from the unresolved short-distance triple-contact realization.
Related
- Local Propagation of Momentum Moments for the Relativistic Vlasov--Poisson System
- Stability in the determination of the coefficients for coupled relativistic Schrödinger system
- Global classical solutions of the repulsive relativistic Vlasov--Poisson system
- Sharp Time Decay and Scattering of Small Data Solutions to the Relativistic Vlasov-Maxwell System
- Sharp blow-up condition for a two-species cross attraction system in 3 or more dimensions
BibTeX
@misc{yoshikawa2026phase,
title = {{Phase Encoding of Genuine Three-Body Interactions in a Relativistic Dirac System in $1+1$ Dimensions}},
author = {Tadashi Yoshikawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25478},
eprint = {2609.25478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25478},
}
RIS
TY - UNPB
TI - Phase Encoding of Genuine Three-Body Interactions in a Relativistic Dirac System in 1+1 Dimensions
AU - Tadashi Yoshikawa
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25478
UR - https://arxiv.org/abs/2609.25478
AB - We show how genuine three-body phase information can enter the invariant mass of a relativistic three-particle Dirac system in (1+1) dimensions. As a solvable reference system, we consider the Sakamoto--Munakata--Ino model with pairwise contact interactions g_ij(1−α_iα_j)δ(x_i−x_j). These singular interactions can be transferred into sector-dependent phases and matching conditions by a discontinuous unitary transformation. Although the explicit contact terms are thereby removed, the nonzero constituent-mass operator is rotated and retains nontrivial spectral information. We introduce a genuine three-body holonomy generated by Q_3=α_1α_2α_3. The kinetic and pair-interaction parts commute with Q_3, while the constituent-mass operator anticommutes with it. Consequently, the massless system separates into the Q_3=±1 sectors, which acquire opposite holonomy phases e^± iθ_3, whereas nonzero constituent masses mix the two sectors. This phase-sector-mixing mechanism makes the relative three-body phase dynamically accessible to the bound-state spectrum and establishes an operator-level mechanism through which the three-body holonomy generates a θ_3 dependence of the physical three-body invariant mass. We further emphasize that the topological three-body holonomy is not automatically equivalent to a bare triple-contact potential; such an equivalence requires a regulated self-adjoint realization and a compatible interaction-dependent boost satisfying the Poincaré algebra. The resulting framework therefore connects genuine three-body phase information to the mass spectrum of a relativistic composite system while clearly separating the controlled holonomy construction from the unresolved short-distance triple-contact realization.
ER -