PreprintCC BY 4.0arXiv
Symmetry Regularization of 1D Generalized Coulomb Problems
Abstract
For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \cite{MMX2025}--we construct two explicit unitary intertwiners ι̂±, the quantum analogs of the classical symmetry regularization maps ι± of \cite{MMX2025}, that unitarily identify each Hκ-energy-definite portion of the Hilbert space L2(ℝ>0,dq) with a unitary lowest-weight representation of SL̃(2,ℝ).
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BibTeX
@misc{bai2026symmetry,
title = {{Symmetry Regularization of 1D Generalized Coulomb Problems}},
author = {Zhanqiang Bai and Junwei Ma and Guowu Meng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.08900},
eprint = {2606.08900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.08900},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry Regularization of 1D Generalized Coulomb Problems
AU - Zhanqiang Bai
AU - Junwei Ma
AU - Guowu Meng
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.08900
UR - https://arxiv.org/abs/2606.08900
AB - For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \cite{MMX2025}--we construct two explicit unitary intertwiners ι̂_±, the quantum analogs of the classical symmetry regularization maps ι_± of \cite{MMX2025}, that unitarily identify each H_κ-energy-definite portion of the Hilbert space L^2(ℝ_>0,dq) with a unitary lowest-weight representation of SL̃(2,ℝ).
ER -