Relating the solutions of the Dirac equation with a background electric potential to solutions with a background pseudoscalar potential

2012/10/21 by Dan Solomon, Solomon, Dan
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Cosmology and Gravitation Theories #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1210.6026

openalex publication_date 2012/10/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We compare two different solutions of the Dirac equation in (1+1) dimensions. One solution is for a fermion in the presence of an electric potential and the other is for a fermion in the presence of a pseudoscalar potential. It is shown that for properly defined potentials one can easily relate the solutions of one system to the solutions of the other. In effect, solving one problem gives the solution to both. In addition, the vacuum charge density is calculated in the both cases and it is shown how this result is impacted by the presence of anomalies in quantum field theory.

Related

• Analytical solutions of a Dirac bound state equation and their field interpretation
• The linear potential and the Dirac equation
• Solutions of the Dirac equation in one-dimensional variable width potential well
• Charge Conjugation, Heavy Ions, e⁺ e^- pairs: Was there a better way to add potentials to Dirac's free electrons?
• Solution of the Dirac equation in presence of an uniform magnetic field