The dynamics of the Einstein-Dirac system. I. A principal bundle formulation of the theory and its canonical analysis Academic Article uri icon

abstract

  • We begin here a mathematical study of the space of globally hyperbolic solutions of the Einstein-Dirac field equations. Our first step is to develop a principal [O(3, 1)] bundle formulation of the Einstein-Dirac fields (which include the spacetime metric represented as a frame field, and a Dirac anticommuting spinor). This formulation provides an invariant description of the fields, and it is useful for controlling their gauge freedom (represented as bundle automorphisms) and for studying the symmetries of solutions (described via Lie derivatives on the bundle). Our analysis of the field equations follows the program developed by Fischer, Marsden, and Moncrief in their study of the vacuum Einstein field equations. We perform a (3 + 1) decomposition of the fields, we obtain a canonical Hamiltonian formulation of the field equations, we study field perturbations, and finally we relate solution symmetries to the kernel of the evolution operator. Some of the mathematies of bundle theory needed to understand this paper is discussed in the appendixes. 1985.

published proceedings

  • Annals of Physics

author list (cited authors)

  • Bao, D., Isenberg, J., & Yasskin, P. B.

citation count

  • 7

complete list of authors

  • Bao, David||Isenberg, James||Yasskin, Philip B

publication date

  • October 1985