The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator

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.

5.3 pages, 3 figures

References in corpus (11)

• Topological energy transfer in an optomechanical system with exceptional points
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
• Playing relativistic billiards beyond graphene
• Relativistic R matrix and continuum shell model
• Revivals of Zitterbewegung of a bound localized Dirac particle
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• Analytic structure of eigenvalues of coupled quantum systems
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Analytic eigenvalue structure of a coupled oscillator system beyond the ground state