非简并狄拉克拉格朗日量的诱导耦合与因果界限
Induced Couplings and Causal Bounds from Nondegenerate Dirac Lagrangians
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中文总结 AI 辅助
研究通过确定狄拉克拉格朗日量的最小零变形，得到双参数旋量双矢量。经规范产生可观测耦合，诱导出偶极算符和守恒流并约束正则化长度，同时应用准则排除多种背景，严格约束非黎曼扇区。
中文摘要 AI 辅助
标准狄拉克拉格朗日量在场导数上是线性的，因此黑塞矩阵为零。我们确定了该拉格朗日量的最小零变形，使协变勒让德映射局部可逆。施加全局相位不变性、实性、适当的庞加莱协变性且无外部背景张量，得到双参数旋量双矢量$\mathcal E^{\mu\nu}=\ell\sigma^{\mu\nu} +\ell_5{}^\star\sigma^{\mu\nu}$。最小$U(1)$规范后，自由零项不再是变分平凡的，诱导出磁偶极和电偶极泡利算符及守恒偶极流。通过精度矩测量可直接约束与物种相关的正则化长度。洛伦兹旋量规范下的度规仿射规范产生对狄拉克算符的自旋曲率、挠率和非度规性修正。应用维洛 - 茨万齐格准则，排除了所有非零纯轴向、纯迹和混合轴向 - 迹挠率背景以及非零纯外尔和二阶迹非度规性背景。仅当有效迹矢量为零时，组合的迹 - 矢量非度规性扇区才不被排除。张量挠率和一般无迹非度规性在无进一步代数假设时仍未分类，而列维 - 奇维塔极限保留度规光锥并仅留下低阶曲率相关质量项。因此，规范勒让德正则狄拉克代表将自由变分模糊性转化为可观测耦合，而非黎曼扇区受因果界限严格约束。
英文摘要
The standard Dirac Lagrangian is linear in the field derivatives and therefore has a vanishing Hessian. We identify the minimal null deformations of this Lagrangian that make the covariant Legendre map locally invertible. Imposing global phase invariance, reality, proper Poincaré covariance, and absence of external background tensors leaves the two-parameter spinorial bivector $\mathcal E^{μν}=\ellσ^{μν} +\ell_5{}^\starσ^{μν}$, where the star denotes the Hodge dual and $\ell^2+\ell_5^2\neq0$. This extends the analysis of \cite{struckmeier2024pauli} by a parity-odd term. After minimal $U(1)$ gauging, this free null term is no longer variationally trivial and induces magnetic- and electric-dipole Pauli operators, together with an identically conserved dipole current. These dipole terms make the species-dependent regularization lengths directly constrainable by precision moment measurements. Metric-affine gauging in a Lorentz-spinor prescription then produces spin-curvature, torsion, and nonmetricity corrections to the Dirac operator. Applying the Velo-Zwanziger criterion, we exclude all nonzero pure axial, pure trace, and mixed axial-trace torsion backgrounds, as well as nonzero pure Weyl and second-trace nonmetricity backgrounds. The combined trace-vector nonmetricity sector is not excluded only when the effective trace vector vanishes. Tensor torsion and general tracefree nonmetricity remain unclassified without further algebraic assumptions, while the Levi-Civita limit preserves the metric light cone and leaves only lower-order curvature-dependent mass terms. Thus, gauging a Legendre-regular Dirac representative turns a free variational ambiguity into observable couplings, while non-Riemannian sectors are sharply constrained by causality bounds.
