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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2603.23051 |
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| _version_ | 1866918446773567488 |
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| author | Yamada, Norikazu |
| author_facet | Yamada, Norikazu |
| contents | Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A kernel-derived orthogonal basis for spectral functions from Euclidean correlators Yamada, Norikazu High Energy Physics - Lattice Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques. |
| title | A kernel-derived orthogonal basis for spectral functions from Euclidean correlators |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2603.23051 |