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

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Journal of Modern Physics 2015年第3期6卷 303-326页

作者： 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 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.

关键词： self-conjugate Hamiltonian Dirac Particle Arbitrary Gravitational Field Schwinger Gauge Kerr Metric

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Pluriharmonic Functions on Bounded Symmetric Domains of C^n

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Chinese Science Bulletin 1993年第17期38卷 1409-1413页

作者：肖建斌 Department-of Mathematics Hunan Normal University

1 Introduction Let Ω be a bounded symmetric domain in the complex vector space Cn, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ0 its isotropy group. It is known that Ω is circular and star-shaped with respect to 0 and that b is circular. The group Γ0 is transitive on b and b has a unique normalized Γ0-invariant measure σ with σ（b）= 1. Hua constructed by group representation theory a system {φkv}

关键词： bounded symmetric domain pluriharmonic function self-conjugate space.

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On the Construction of the conjugate Hull of Brandt Semigroups

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Acta Mathematica Sinica,English Series 1998年第4期14卷 519-526页

作者： Zhang Moucheng, Department of Mathematics, South China Normal University, Guangzhou 510631, ChinaKan Haibing, Institute of Mathematics, Fudan University, Shanghai 200433, ChinaLi Yonghua, Department of Mathematics, Yunnan University, Kunming 650000, China Department of Mathematics, South China Normal University, Guangzhou 510631, China Department of Mathematics South China Normal University 510631 Guangzhou China

In this paper the characterizations of conjugate hulls Ψ(S), φ(S), T(S) and θ(S) on a Brandt semigroup S are given. By using these results we can prove that T(S) is self-conjugate in Ψ(S) for a Brandt semigroup S.

关键词： conjugate hull self-conjugate Linked bitranslation Brandt semigroup

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