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

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

2011-07-05

arxiv.org/abs/1107.0844v5

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

39 pages

Scientific paper

We have proposed previously a procedure for constructing self-conjugate Hamiltonians $H_{\eta} $ in the $\eta $-representation with 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 quantities $H_{\eta} $ can be obtained in particular using "reduced" parts of Dirac Hamiltonians, i.e. expressions for Dirac Hamiltonians derived at use of tetrad vectors in the Schwinger gauge without or with small numbers of summands with bispinor connectivities. With a glance of these results we propose the modified method of construction of Hamiltonians in the $\eta $-representation with a significantly smaller amount of required calculations. Using the proposed procedure, in this paper we for the first time find self-conjugate Hamiltonians for a number of metrics, including the Kerr metric in coordinates of the Boyer-Lindquist, the Eddington-Finkelstein, Finkelstein-Lemaitre, Kruskal metrics, and metrics of the Clifford torus geometry.

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