| Revista: | Brazilian journal of physics |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000328617 |
| ISSN: | 0103-9733 |
| Autores: | Arminjon, Mayeul1 Reifler, Frank2 |
| Instituciones: | 1Centre National de la Recherche Scientifique, Section of Theoretical Physics, Grenoble, Isere. Francia 2Lockheed Martin Corporation, Moorestown, New Jersey. Estados Unidos de América |
| Año: | 2010 |
| Periodo: | Jun |
| Volumen: | 40 |
| Número: | 2 |
| Paginación: | 242-255 |
| País: | Brasil |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Experimental |
| Resumen en inglés | We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, iff the field of Dirac matrices γµ satisfies a specific PDE. This equation is always satisfied for DFW with its restricted choice for the γµ matrices. It similarly restricts the choice of the γµ matrices for TRD. However, this restriction can be achieved. The frame dependence of a general Hamiltonian operator is studied. We show that in any given reference frame with minor restrictions on the spacetime metric, the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product. Finally, the condition for the general Dirac Hamiltonian operator to be Hermitian is derived in a general curved spacetime. For DFW, the validity of this hermiticity condition depends on the choice of the γµ matrices |
| Disciplinas: | Física y astronomía |
| Palabras clave: | Física, Física de partículas y campos cuánticos, Ecuación de Dirac, Gravitación, Conservación de corriente, Hamiltoniana hermitiana, Tensores |
| Keyword: | Physics and astronomy, Particle physics and quantum fields, Physics, Dirac equation, Gravitation, Current conservation, Hermitian Hamiltonian, tensor representation |
| Texto completo: | Texto completo (Ver HTML) |
