Analysis of the Feynman-Gell-Mann version of the Dirac equation

• Grant number: 19/06734-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2019
• End date: December 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Antonio Soares de Castro
• Grantee: Vitor Bentes Mendrot
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

The Feynman-Gell-Mann version of the Dirac equation in 3+1 dimensions presents itself as a second-order equation and two components for the vector interaction. That alternative version of the Dirac equation is certainly a valuable tool for approaching the planar behavior of relativistic quantum systems and might resolve doubts relating spin as an independent degree of freedom in 2+1 dimensions. For exploring that quadratic version of the Dirac equation the student should be knowledgeable about relativistic quantum mechanics. To do so, he should first familiarize himself with the Klein-Gordon equation. After this the student can enquiry into the meaning and implications of the Dirac equation, and he will do this considering 3 + 1, 2 + 1 and 1 + 1 dimensions. Next, the student will generalize the Feynman-Gell-Mann version of the Dirac equation to include other forms of interactions beyond the vector interaction. The next step will be the confrontation between the use of Feynman-Gell-Mann formulation and the usual formulation for several systems usually explored in the literature.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MENDROT, V. B.; DE CASTRO, A. S.. Comment on 'The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass'. Journal of Physics A-Mathematical and Theoretical, v. 54, n. 2, p. 2-pg., 2021-01-15. (19/06734-2)

MENDROT, V. B.; DE CASTRO, A. S.. Comment on ``Energy Spectrum of a Dirac Particle with Position-Dependent Mass Under the Influence of the Aharonov-Casher Effect{''}. Brazilian Journal of Physics, v. 51, n. 1, p. 19-21, FEB 2021. (19/06734-2)