Representations of the Dirac wave function in a curved spacetime
General Relativity and Quantum Cosmology
2011-10-05 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove theorems that relate together the different representations and the different choices of connections. In particular, the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the Dirac equation for a vector wave function, in the same spacetime.
Keywords
Cite
@article{arxiv.1011.6286,
title = {Representations of the Dirac wave function in a curved spacetime},
author = {Mayeul Arminjon and Frank Reifler},
journal= {arXiv preprint arXiv:1011.6286},
year = {2011}
}
Comments
14 pages (standard 12pt article). Text of a talk given at DICE2010: "Space-Time-Matter - current issues in quantum mechanics and beyond" (Castiglioncello, Italy, September 13-17, 2010)