Emergence of the polydeterminant in QCD

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Giacosa F., Zakrzewski M., Jafarzade S., Pisarski R. D.

Letters in Mathematical Physics, vol.115, no.6, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Nəşrin Növü: Article / Article
  • Cild: 115 Say: 6
  • Nəşr tarixi: 2025
  • Doi nömrəsi: 10.1007/s11005-025-02000-4
  • jurnalın adı: Letters in Mathematical Physics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Açar sözlər: Chiral anomaly, Effective field theories, Mixed discriminant, Polydeterminant, Quantum chromodynamics
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N×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.