2014/07/31 by R. V. Maluf, J. E. G. Silva, W. T. Cruz +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Dirac algebra #Dirac equation #Dirac spinor #Hamiltonian (control theory) #Hydrogen atom #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Spinor #Theoretical physics #Theory of relativity #hep-th
paper · pdf · doi:10.1016/j.physletb.2014.09.059
published as Phys. Lett. B 738, 341-345 (2014) · Revtex style, 13 pages, 1 table, references added, improved text, published in PLB
openalex publication_date 2014/09/30 · arxiv created 2014/10/20 · arxiv updated 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work, we study the modified Dirac equation in the framework of very special relativity (VSR). The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that achieved from the Standard Model Extension (SME) via coupling of the spinor field to a Lorentz-violating term, but new features arise inherited from the non-local character of the VSR. In addition, the implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen atom are determined by calculating the first-order energy corrections in the context of standard quantum mechanics. Among the results, we highlight that the modified Hamiltonian provides non-vanishing corrections which lift the degeneracy of the energy levels and allow us to find an upper bound upon the VSR-parameter.