Emergence of the polydeterminant in QCD
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908572465496064 |
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| author | Giacosa, Francesco Zakrzewski, Michał Jafarzade, Shahriyar Pisarski, Robert D. |
| author_facet | Giacosa, Francesco Zakrzewski, Michał Jafarzade, Shahriyar Pisarski, Robert D. |
| contents | A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in Quantum Chromodynamics (PRD 97 (2018) 9, 091901 PRD 109 (2024) 7, L071502), in particular in connection to mesons. This \textit{polydeterminant function}, known in the mathematical literature as a mixed discriminant, associates $N$ distinct $N\times N$ complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergence of the polydeterminant in QCD Giacosa, Francesco Zakrzewski, Michał Jafarzade, Shahriyar Pisarski, Robert D. Mathematical Physics High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in Quantum Chromodynamics (PRD 97 (2018) 9, 091901 PRD 109 (2024) 7, L071502), in particular in connection to mesons. This \textit{polydeterminant function}, known in the mathematical literature as a mixed discriminant, associates $N$ distinct $N\times N$ complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown. |
| title | Emergence of the polydeterminant in QCD |
| topic | Mathematical Physics High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.15617 |