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V. P. Neznamov - One of the best experts on this subject based on the ideXlab platform.
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Some Aspects of Quantum Mechanics of Particle Motion in Static Centrally Symmetric Gravitational Fields
arXiv: General Relativity and Quantum Cosmology, 2015Co-Authors: M.v. Gorbatenko, V. P. Neznamov, E. Yu. PopovAbstract:The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric Gravitational Fields are analyzed by taking into account the Hilbert causality condition. For all the explored metrics, assuming existence of event horizons, the conditions of a "fall" of a particle to the appropriate event horizons are implemented. The exclusion is one of the solutions for the Reissner-Nordstroem extreme field with the single event horizon. In this case, while fulfilling the condition found by V.I.Dokuchaev, Yu.N.Yeroshenko, the normalization integral is convergent and the wave functions become zero on the event horizon. This corresponds to the Hilbert causality condition. In our paper, due to the analysis of the effective potential for the Reissner-Nordstroem extreme field with real radial wave functions of the Dirac equation, the impossibility is demonstrated for the bound stationary state existence of quantum-mechanical particles, with positive energy, off the event horizon. The analysis of the effective potential of the Dirac equation for the case of the naked singularity of the Reissner-Nordstroem field shown the possible existence of stationary bound states of quantum-mechanical half-spin particles.
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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
Journal of Modern Physics, 2015Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract: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.
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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
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract: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.
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uniqueness and self conjugacy of dirac hamiltonians in arbitrary Gravitational Fields
Physical Review D, 2011Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract:Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows for describing the Dirac particles motion in arbitrary stationary Gravitational Fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the {eta} representation gives the transformation of the Schroedinger equation for the nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the {eta} representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.
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solution of the problem of uniqueness and hermiticity of hamiltonians for dirac particles in Gravitational Fields
Physical Review D, 2010Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract:The authors prove that the dynamics of spin 1/2 particles in stationary Gravitational Fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the Gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary Gravitational Fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.
Alan R Steif - One of the best experts on this subject based on the ideXlab platform.
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strings in strong Gravitational Fields
Physical Review D, 1990Co-Authors: Gary T Horowitz, Alan R SteifAbstract:String propagation in exact plane-wave solutions (with nonzero axion and dilaton Fields) is analyzed. In these backgrounds, strings can undergo transitions from one state to another. Selection rules are derived which describe allowed and forbidden transitions of the string. It is shown that singular plane waves result in infinitely excited strings. An example is given of a solution whose singular properties are the opposite of an orbifold: it is geodesically complete, but still singular from the standpoint of string theory. Some implications of these results are discussed.
Giorgio Papini - One of the best experts on this subject based on the ideXlab platform.
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quantum systems in weak Gravitational Fields
aibq, 2002Co-Authors: Giorgio PapiniAbstract:Fully covariant wave equations predict the existence of a class of inertial-Gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical Fields, but, by conforming to general relativity, provide very valuable information on how Einstein’s views carry through in the world of the quantum. Experiments already confirm that inertia and Newtonian gravity affect quantum particles in ways that are fully consistent with general relativity down to distances of ∼ 10–4 cm for superconducting electrons [1] and of ∼ 10-8 cm for neutrons [2, 3, 4]. Other aspects of the interaction of gravity with quantum systems are just beginning to be investigated.
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quantum systems in weak Gravitational Fields
arXiv: General Relativity and Quantum Cosmology, 2001Co-Authors: Giorgio PapiniAbstract:Fully covariant wave equations predict the existence of a class of inertial-Gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical Fields, but, by conforming to general relativity, provide very valuable information on how Einstein's views carry through in the world of the quantum.
M.v. Gorbatenko - One of the best experts on this subject based on the ideXlab platform.
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Some Aspects of Quantum Mechanics of Particle Motion in Static Centrally Symmetric Gravitational Fields
arXiv: General Relativity and Quantum Cosmology, 2015Co-Authors: M.v. Gorbatenko, V. P. Neznamov, E. Yu. PopovAbstract:The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric Gravitational Fields are analyzed by taking into account the Hilbert causality condition. For all the explored metrics, assuming existence of event horizons, the conditions of a "fall" of a particle to the appropriate event horizons are implemented. The exclusion is one of the solutions for the Reissner-Nordstroem extreme field with the single event horizon. In this case, while fulfilling the condition found by V.I.Dokuchaev, Yu.N.Yeroshenko, the normalization integral is convergent and the wave functions become zero on the event horizon. This corresponds to the Hilbert causality condition. In our paper, due to the analysis of the effective potential for the Reissner-Nordstroem extreme field with real radial wave functions of the Dirac equation, the impossibility is demonstrated for the bound stationary state existence of quantum-mechanical particles, with positive energy, off the event horizon. The analysis of the effective potential of the Dirac equation for the case of the naked singularity of the Reissner-Nordstroem field shown the possible existence of stationary bound states of quantum-mechanical half-spin particles.
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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
Journal of Modern Physics, 2015Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract: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.
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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
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract: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.
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uniqueness and self conjugacy of dirac hamiltonians in arbitrary Gravitational Fields
Physical Review D, 2011Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract:Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows for describing the Dirac particles motion in arbitrary stationary Gravitational Fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the {eta} representation gives the transformation of the Schroedinger equation for the nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the {eta} representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.
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solution of the problem of uniqueness and hermiticity of hamiltonians for dirac particles in Gravitational Fields
Physical Review D, 2010Co-Authors: M.v. Gorbatenko, V. P. NeznamovAbstract:The authors prove that the dynamics of spin 1/2 particles in stationary Gravitational Fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the Gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary Gravitational Fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.
Gary T Horowitz - One of the best experts on this subject based on the ideXlab platform.
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strings in strong Gravitational Fields
Physical Review D, 1990Co-Authors: Gary T Horowitz, Alan R SteifAbstract:String propagation in exact plane-wave solutions (with nonzero axion and dilaton Fields) is analyzed. In these backgrounds, strings can undergo transitions from one state to another. Selection rules are derived which describe allowed and forbidden transitions of the string. It is shown that singular plane waves result in infinitely excited strings. An example is given of a solution whose singular properties are the opposite of an orbifold: it is geodesically complete, but still singular from the standpoint of string theory. Some implications of these results are discussed.
