Tree-Level Interaction Vertices in the Linear Sigma Model with Quarks under Global Rotation
Abstract
We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.
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BibTeX
@misc{hernandez2026treelevel,
title = {{Tree-Level Interaction Vertices in the Linear Sigma Model with Quarks under Global Rotation}},
author = {Luis A. Hernández and Eduardo Lazcano and R. Zamora},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01760},
eprint = {2610.01760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01760},
}
RIS
TY - UNPB
TI - Tree-Level Interaction Vertices in the Linear Sigma Model with Quarks under Global Rotation
AU - Luis A. Hernández
AU - Eduardo Lazcano
AU - R. Zamora
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01760
UR - https://arxiv.org/abs/2610.01760
AB - We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.
ER -