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arXiv · 1908.09352

The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator

Bo-Xing Cao·Fu-Lin Zhang
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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.

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Bo-Xing Cao, Fu-Lin Zhang. 2019-08-25. The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator. https://doi.org/10.1088/0256-307x%2F37%2F9%2F090303

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