2023/08/28 by Hisakazu Minakata, Minakata, Hisakazu
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Molecular Spectroscopy and Structure #Neutrino Physics Research
paper · pdf · doi:10.48550/arxiv.2308.14501
openalex publication_date 2023/08/28 · openalex created_date 2023/08/31 · openalex updated_date 2026/07/28
The S matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given S matrix which describes neutrino oscillation, one can define the two different rephased amplitudes Sαβ Reph-1 ≡ e^ i (λ1 / 2E) x Sαβ and Sαβ Reph-2 ≡ e^ i (λ2 / 2E) x Sαβ, which are physically equivalent to each other, where λk / 2E denotes the energy eigenvalue of the k-th mass eigenstate. We point out that the transformation of the reparametrization (Rep) symmetry obtained with ``Symmetry Finder'' maps Sαβ Reph-1 to Sαβ Reph-2 , and vice versa, providing a local and manifest realization of the S matrix rephasing invariance by the Rep symmetry of the 1-2 state exchange type. It is strongly indicative of quantum mechanical nature of the Rep symmetry. The rephasing and Rep symmetry relation, though its all-order treatment remains incomplete, is shown to imply absence of the pure 1-3 exchange symmetry in Denton~\it et al.~perturbation theory. It then triggers a study of convergence of perturbation series.