1107.0844 (M. V. Gorbatenko et al.)

A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in
Arbitrary Gravitational Fields and Its Application to Centrally and Axially
Symmetric Gravitational Fields    [PDF]

M. V. Gorbatenko, V. P. Neznamov

We have proposed previously a method for constructing self-conjugate Hamiltonians H_eta in the eta-representation with a flat scalar product to describe the dynamics of Dirac particles in arbitrary gravitational fields. In this paper, we prove that, for block-diagonal metrics, the Hamiltonians H_eta can be obtained, in particular, using "reduced" parts of Dirac Hamiltonians, i.e. expressions for Dirac Hamiltonians derived using tetrad vectors in the Schwinger gauge without or with a few summands with bispinor connectivities. Based on these results, we propose a modified method for constructing Hamiltonians in the eta-representation with a significantly smaller amount of required calculations. Using this method, here we for the first time find self-conjugate Hamiltonians for a number of metrics, including the Kerr metric in the Boyer-Lindquist coordinates, the Eddington-Finkelstein, Finkelstein-Lemaitre, Kruskal, Clifford torus metrics and for non-stationary metrics of open and spatially flat Friedmann models.

View original: http://arxiv.org/abs/1107.0844