TITLE:
A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields
AUTHORS:
M. V. Gorbatenko, V. P. Neznamov
KEYWORDS:
Self-Conjugate Hamiltonian, Dirac Particle, Arbitrary Gravitational Field, Schwinger Gauge, Kerr Metric
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.3,
February
27,
2015
ABSTRACT: We have
proposed previously a method for constructing self-conjugate Hamiltonians Hh 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 Hh 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.