2024/12/04 by Tae‐Yeon Kim, Kim, Taeyeon, Piljin Yi +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2412.03667
openalex publication_date 2024/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general covariance demands us to use the Lie derivative. We argue that, with this alone and without any further tweaking, the Noether energy-momentum \mathbbT must equal the symmetric counterpart, T, inevitably and show the equality explicitly for general tensors. For spinors, a subtlety with the Lie derivative itself enters the issue and leads us to the Kosmann lift, often unnoticed by the physics community, from which T=\mathbbT again emerges straightforwardly and in a naturally symmetric form. Finally, we address how the same Kosmann lift affects the anomaly computations and show that the diffeomorphism anomaly from the seminal paper must be halved, while the venerable anomaly polynomials themselves stand unaffected. We discuss the ramifications of these findings.