| 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. | |
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