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TMF, 2001, Volume 126, Number 1, Pages 115–124 (Mi tmf418)  

This article is cited in 18 scientific papers (total in 18 papers)

Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Hamiltonian Diagonalization Method

Yu. V. Pavlov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We diagonalize the metric Hamiltonian and evaluate the energy spectrum of the corresponding quasiparticles for a scalar field coupled to a curvature in the case of an $N$-dimensional homogeneous isotropic space. The energy spectrum for the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian is also evaluated. We construct a modified energy-momentum tensor with the following properties: for the conformal scalar field, it coincides with the metric energy-momentum tensor; the energies of the particles corresponding to its diagonal form are equal to the oscillator frequency; and the number of such particles created in a nonstationary metric is finite. We show that the Hamiltonian defined by the modified energy-momentum tensor can be obtained as the canonical Hamiltonian under a certain choice of variables.


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English version:
Theoretical and Mathematical Physics, 2001, 126:1, 92–100

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Received: 19.06.2000

Citation: Yu. V. Pavlov, “Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Hamiltonian Diagonalization Method”, TMF, 126:1 (2001), 115–124; Theoret. and Math. Phys., 126:1 (2001), 92–100

Citation in format AMSBIB
\by Yu.~V.~Pavlov
\paper Nonconformal Scalar Field in a Homogeneous Isotropic Space and the Hamiltonian Diagonalization Method
\jour TMF
\yr 2001
\vol 126
\issue 1
\pages 115--124
\jour Theoret. and Math. Phys.
\yr 2001
\vol 126
\issue 1
\pages 92--100

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    This publication is cited in the following articles:
    1. Yu. V. Pavlov, “Dimensional Regularization and the $n$-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces”, Theoret. and Math. Phys., 128:2 (2001), 1034–1045  mathnet  crossref  crossref  zmath  isi
    2. Pavlov, YV, “Creation of the nonconformal scalar particles in nonstationary metric”, International Journal of Modern Physics A, 17:6–7 (2002), 1041  crossref  mathscinet  adsnasa  isi
    3. K. S. Mamaeva, N. N. Trunov, “Wave Equations in Riemannian Spaces”, Theoret. and Math. Phys., 135:1 (2003), 520–530  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Yu. V. Pavlov, “The $n$-Wave Procedure and Dimensional Regularization for the Scalar Field in a Homogeneous Isotropic Space”, Theoret. and Math. Phys., 138:3 (2004), 383–396  mathnet  crossref  crossref  adsnasa  isi
    5. Grib A.A., Pavlov Yu.V., “Quantum field theory in curved spacetime and the dark matter problem”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, 2007, 96–106  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Grib, AA, “Is Dark Matter the Relic of the Primordial Matter That Created the Visible Matter of the Universe?”, Gravitation & Cosmology, 14:1 (2008), 1  crossref  zmath  adsnasa  isi
    7. Pavlov, YV, “Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field”, Gravitation & Cosmology, 14:4 (2008), 314  crossref  mathscinet  zmath  adsnasa  isi
    8. Batista, AB, “Particle Production in an Expanding Universe Dominated by Dark Energy Fluid”, Gravitation & Cosmology, 14:2 (2008), 140  crossref  mathscinet  zmath  adsnasa  isi
    9. Pavlov, YV, “On particle creation and renormalization in a cosmological model with a Big Rip”, Gravitation & Cosmology, 15:4 (2009), 341  crossref  zmath  adsnasa  isi  scopus  scopus
    10. Pereira S.H., Bessa C.H.G., Lima J.A.S., “Quantized fields and gravitational particle creation in f (R) expanding universes”, Phys Lett B, 690:2 (2010), 103–107  crossref  adsnasa  isi  elib  scopus  scopus
    11. Houndjo M.J.S., Monwanou A.V., Orou J.B.Ch., “Quantum Effects From Particle Production on Background Evolution and Cardy-Verlinde Formula in F(R) Gravity”, Internat J Modern Phys D, 20:13 (2011), 2449–2469  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. Yu. V. Pavlov, “Tochnye resheniya dlya skalyarnogo polya v odnorodnykh izotropnykh kosmologicheskikh modelyakh i rozhdenie chastits”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 153, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2011, 65–71  mathnet
    13. Yu. V. Pavlov, “Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models”, Theoret. and Math. Phys., 174:3 (2013), 438–445  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Jesus J.F. Pereira S.H., “Ccdm Model From Quantum Particle Creation: Constraints on Dark Matter Mass”, J. Cosmol. Astropart. Phys., 2014, no. 7, 040  crossref  isi  scopus  scopus
    15. Pereira S.H., Holanda R.F.L., “Particle Creation in a F(R) Theory With Cosmological Constraints”, Gen. Relativ. Gravit., 46:4 (2014), 1699  crossref  zmath  adsnasa  isi  scopus  scopus
    16. Pavlov Yu.V., “On Creation of Scalar Particles With Gauss-Bonnet Type Coupling To Curvature in Friedmann Cosmological Models”, Gravit. Cosmol., 20:1 (2014), 21–25  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    17. Grib A.A. Pavlov Yu.V., “Particle creation in the early Universe: Achievements and problems”, Gravit. Cosmol., 22:2 (2016), 107–115  crossref  mathscinet  zmath  isi  scopus
    18. Rashidi R., Ahmadi F., Setare M.R., “Particle Creation in the Framework of F (G) Gravity”, Astrophys. Space Sci., 363:9 (2018), 196  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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