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

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.

DOI: https://doi.org/10.4213/tmf418

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

Bibliographic databases:

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
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• https://doi.org/10.4213/tmf418
• http://mi.mathnet.ru/eng/tmf/v126/i1/p115

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Pavlov, YV, “Creation of the nonconformal scalar particles in nonstationary metric”, International Journal of Modern Physics A, 17:6–7 (2002), 1041
3. K. S. Mamaeva, N. N. Trunov, “Wave Equations in Riemannian Spaces”, Theoret. and Math. Phys., 135:1 (2003), 520–530
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
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
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
7. Pavlov, YV, “Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field”, Gravitation & Cosmology, 14:4 (2008), 314
8. Batista, AB, “Particle Production in an Expanding Universe Dominated by Dark Energy Fluid”, Gravitation & Cosmology, 14:2 (2008), 140
9. Pavlov, YV, “On particle creation and renormalization in a cosmological model with a Big Rip”, Gravitation & Cosmology, 15:4 (2009), 341
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
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
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
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
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
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
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
17. Grib A.A. Pavlov Yu.V., “Particle creation in the early Universe: Achievements and problems”, Gravit. Cosmol., 22:2 (2016), 107–115
18. Rashidi R., Ahmadi F., Setare M.R., “Particle Creation in the Framework of F (G) Gravity”, Astrophys. Space Sci., 363:9 (2018), 196
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