Author(s)

M. V. Gorbatenko, V. P. Neznamov^*

Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Sarov, Russia.

We have proposed previously a method for constructing self-conjugate Hamiltonians H_h in the h-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_h 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 h-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.

Self-Conjugate Hamiltonian, Dirac Particle, Arbitrary Gravitational Field, Schwinger Gauge, Kerr Metric

Gorbatenko, M. and Neznamov, V. (2015) A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields. Journal of Modern Physics, 6, 303-326. doi: 10.4236/jmp.2015.63034.