The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator

We study the analytic structure for the eigenvalues of the one-dimensional Dirac oscillator,by analytically continning 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.