English

The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator

Quantum Physics 2020-09-02 v3

Abstract

We study the analytic structure for the eigenvalues of the one-dimensional Dirac oscillator, by analytically continuing its frequency on the complex plane. A twofold Riemann surface is found, connecting the two states of a pair of particle and antiparticle. One can, at least in principle, accomplish the transition from a positive energy state to its antiparticle state by moving the frequency continuously on the complex plane, without changing the Hamiltonian after transition. This result provides a visual explanation for the absence of a negative energy state with the quantum number n=0.

Keywords

Cite

@article{arxiv.1908.09352,
  title  = {The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator},
  author = {Bo-Xing Cao and Fu-Lin Zhang},
  journal= {arXiv preprint arXiv:1908.09352},
  year   = {2020}
}

Comments

5.3 pages, 3 figures

R2 v1 2026-06-23T10:56:15.891Z