| Revista: | Revista mexicana de física |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000380704 |
| ISSN: | 0035-001X |
| Autores: | Vincenzo, S., de1 |
| Instituciones: | 1Universidad Central de Venezuela, Facultad de Ciencias, Caracas, Distrito Federal. Venezuela |
| Año: | 2014 |
| Periodo: | Sep-Oct |
| Volumen: | 60 |
| Número: | 5 |
| Paginación: | 401-408 |
| País: | México |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Analítico, teórico |
| Resumen en inglés | We introduce a family of four Dirac operators in 1+1 dimensions: ĥA = -iħc^ΓA ∂/∂x (A = 1, 2, 3,4) for x ∉ Ω = [α, b]. Here, {^ΓA} is a complete set of 2 x 2 matrices: ^Γ1 = ^1, ^Γ2 = ^α, ^Γ3 = ^β, and ^Γ4 = i^β^α, where ^α and ^β are the usual Dirac matrices. We show that the hermiticity of each of the operators ĥA implies that CA (x = b) = CA (x = α), where the real-valued quantities CA = cψ†^ΓAψ, the bilinear densities, are precisely the components of a Clifford number Ĉ in the basis of the matrices ^ΓA; moreover, Ĉ/2cρ is a density matrix (ρ is the probability density). Because we know the most general family of self-adjoint boundary conditions for ĥ2 in the Weyl representation (and also for ĥ1), we can obtain similar families for ĥ3 and ĥ4 in the Weyl representation using only the aforementioned family for ĥ2 and changes of representation among the Dirac matrices. Using these results, we also determine families of general boundary conditions for all these operators in the standard representation. We also find and discuss connections between boundary conditions for the free (self-adjoint) Dirac Hamiltonian in the standard representation and boundary conditions for the free Dirac Hamiltonian in the Foldy-Wouthuysen representation |
| Disciplinas: | Física y astronomía |
| Palabras clave: | Física, Dirac, Densidades bilineares, Cambios de representación, Condiciones límite, Representación Foldy-Wouthuysen |
| Keyword: | Physics and astronomy, Physics, Dirac, Bilinear densities, Changes of representation, Boundary conditions, Foldy-Wouthuysen representation |
| Texto completo: | Texto completo (Ver PDF) |
