Representations of the Dirac wave function in a curved spacetime

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.

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)

References in corpus (2)

• Dirac-type equations in a gravitational field, with vector wave function
• Four-vector vs. four-scalar representation of the Dirac wave function

Cited by in corpus (1)

• Quantum Back Flow Across a Black Hole Horizon in a Toy Model Approach