Spinor fields in Bianchi type-I universe

Physics of Particles and Nuclei

Volumn 37, Issue SUPPL. 1, 2006, Pages

  Saha, B ^a  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751574918     PISSN: 10637796     EISSN: 15318559     Source Type: Journal    
DOI: 10.1134/S1063779606070021     Document Type: Article

References (105)

1. A. F. Ranada, "Classical Nonlinear Dirac Field Models of Extended Particles," in Quantum Theory, Groups, Fields and Particles, Ed. by A. O. Barut (Reidel, Dordrecht, 1983), pp. 271-291.
2. D. D. Ivanenko, "Introduction to the Elementray Particle Theory," Usp. Fiz. Nauk. 32 (2), 149-184 (1947).
3. D. D. Ivanenko, "Introduction to the Elementray Particle Theory," Usp. Fiz. Nauk. 32 (3), 261-315 (1947).
4. V. Rodichev, "Twisted Space and Nonlinear Field Equations," Zh. Eksp. Teor. Fiz. 40, 1469-1472 (1961)
5. [Sov. Phys. JETP 13, 1029 (1961)].
6. H. Weyl, "A Remark on the Coupling of Gravitation and Electron," Phys. Rev. 77, 699-701 (1950).
7. R. Utiyama, "Invariant Theoretical Interpretation of Interaction," Phys. Rev. 101, 1597-1607 (1956).
8. T. W. B. Kibble, "Lorentz Invariance and the Gravitational Filed," J. Math. Phys. 2, 212-221 (1961).
9. D. W. Sciama, Festschrift for Infeld (Pergamon, Oxford, 1960), pp. 415-439.
10. A. F. Ranada and M. Soler, "Elementary Spinorial Excitations in a Model Universe," J. Math. Phys. 13, 671-675 (1972).
11. F. W. Hehl, P. Heyde, and G. D. Kerlick, "General Relativity with Spin and Torsion: Foundations and Prospects," Rev. Mod. Phys. 48, 393-416 (1976).
12. W. Heisenberg, "Doubts and Hopes in Quantum-Electrodynamics," Physica 19, 897-908 (1953).
13. W. Heisenberg, "Quantum Theory of Fields and Elementary Particles," Rev. Mod. Phys. 29 (3), 269-278 (1957).
14. D. J. Gross and A. Neveu, "Dynamical Symmetry Breaking in Asymptotically Free Field Theories," Phys. Rev. D 10, 3235-3253 (1974).
15. R. Finkelstein, R. LeLevier, and M. Ruderman, "Nonlinear Spinor Fields," Phys. Rev. 83, 326-332 (1951).
16. C. Armendáriz-Picón and P. B. Greene, "Spinors, Inflation, and Non-Singular Cyclic Cosmologies," Gen. Relativ. Gravit. 35, 1637-1658 (2003).
17. L. Parker, "Quantized Fields and Particle Creation in Expanding Universes. I," Phys. Rev. 183, 1057-1068 (1969).
18. L. Parker, "Quantized Fields and Particle Creation in Expanding Universes. II," Phys. Rev. D 3, 346-356 (1971).
19. C. W. Misner, "The Isotropy of the Universe," Astrophys. J. 151, 431-457 (1968).
20. Ya. B. Zel'dovich, "Creation of Particles in Cosmology," Pis'maZh. Eksp. Teor. Fiz. 12, 443 (1970)
21. [JETP Lett. 12, 307 (1970)].
22. V. N. Lukash and A. A. Starobinsky, "Isotropization of Cosmological Expansion Due to Particle Production," Zh. Eksp. Teor. Fiz. 66, 1515 (1974)
23. [Sov. Phys. JETP 39, 742 (1974)].
24. V. N. Lukash, I. D. Novikov, A. A. Starobinsky, and Ya. B. Zel'dovich, "Quantum Effects and Evolution of Cosmological Models," Nuovo Cimento 35, 293-307 (1976).
25. B. L. Hu and L. Parker, "Anisotropy Damping Through Quantum Effects in the Early Universe," Phys. Rev. D 17, 933-945 (1978).
26. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifshitz, "Oscillatory Approach to a Singular Point in the Relativistic Cosmology," Adv. Phys. 19, 525-573 (1970).
27. K. C. Jacobs, "Spatially Homogeneous and Euclidean Cosmological Models with Shear," Astrophys. J. 153, 661-678 (1968).
28. L. P. Chimento and M. S. Mollerach, "Dirac Equation in Bianchi I Metrics," Phys. Lett. A 121 (1), 7-10 (1987).
29. M. A. Castagnino, C. D. El Hasi, F. D. Mazzitelli, and J. P. Paz, "On the Dirac Equation in Anisotropic Backgrounds," Phys. Lett. A128 (1), 25-28 (1988).
30. M. Henneaux, "Bianchi Type-I Cosmologies and Spinor Fields," Phys. Rev. D 21, 857-863 (1980).
31. M. Henneaux, "Univers De Bianchi Et Champs Spinoriels," Ann. Inst. Henri Poincaré 34, 329-349 (1981).
32. B. L. Hu, "Gravitational Waves in a Bianchi Type-I Universe," Phys. Rev. D 18, 969-982 (1978).
33. P. G. Miedema and W. A. van Leeuwen, "Cosmological Perturbations in Bianchi Type-I Universes," Phys. Rev. D 47, 3151-3164 (1993).
34. H. T. Cho and A. D. Speliotopoulos, "Gravitational Waves in Bianchi Type-I Universes: The Classical Theory," Phys. Rev. D 5, 5445-5458 (1995).
35. G. N. Shikin, "Nonlinear Spinor Fields in External Cosmological Field and the Problem of Elimination of Initial Singularity," Preprint No. 19, IPBRAE (Academy of Science of USSR, 1991), pp. 1-21.
36. Yu. P. Rybakov, B. Saha, and G. N. Shikin, "Nonlinear Spinor Field in External Bianchi-I Type Gravitational Field and the Problem of Eliminating Initial Singularity," PFU Rep., Phys. 2 (2), 61-78 (1994).
37. Yu. P. Rybakov, B. Saha, and G. N. Shikin, "Exact Self-Consistent Solutions to Nonlinear Spinor Field Equations in Bianchi Type-I Space-Time," Commun. Theor. Phys. 3, 199-210 (1994).
38. B. Saha and G. N. Shikin, "Nonlinear Spinor Field in Bianchi Type-I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions," J. Math. Phys. 38, 5305-5318 (1997).
39. R. Alvarado, Yu. P. Rybakov, B. Saha, and G. N. Shikin, "Exact Self-Consistent Solutions to the Interacting Spinor and Scalar Field Equations in Bianchi Type-I Space-Time," Commun. Theor. Phys. 4, 247-262 (1995).
40. R. Alvarado, Yu. P. Rybakov, B. Saha, and G. N. Shikin, "Interacting Spinor and Scalar Fields in Bianchi Type-I Space-Time: Exact Self-Consistent Solutions," Izv. Vyssh. Uchebn. Zaved., Fiz. 38, 53-58 (1995).
41. B. Saha and G. N. Shikin, "Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-Consistent Solutions," Gen. Relativ. Gravit. 29, 199-1112 (1997); gr-gc/9609056.
42. B. Saha and G. N. Shikin, "On the Role of A Term in the Evolution of Bianchi-I Cosmological Model with Nonlinear Spinor Field," PFU Rep., Phys., No. 8, 17-20 (2000).
43. B Saha, "Dirac Spinor in Bianchi-I Universe with time dependent Gravitational and Cosmological Constants," Mod. Phys. Lett. A16, 1287-1296 (2001).
44. A. Einstein, "Kosmologische Betrachtungen Zur Allgemeinen Relativita Tstheorie," Sitzungsber. Preuss. Acad. Wiss. 1, 142-152 (1917).
45. A. Einstein, "Spielen Die Gravitationsfelder Im Aufbau Der Materiellen Elementarteilchen Eine Wesentliche Rolle?," Sitzungsber. Preuss. Acad. Wiss. 1, 349-356 (1919).
46. M. Tsamparlis and P. S. Apostolopoulos, "Symmetries of Blanchi I Space-Times," J. Math. Phys. 41, 7573-7588 (2000).
47. G. F. R. Ellis, "Dynamics of Pressure-Free Matter in General Relativity," J. Math. Phys. 8 (5), 1171-1194 (1967).
48. J. M. Stewart and G. F. R. Ellis, "Solutions of Einstein's Equations for a Fluid Which Exhibit Local Rotational Symmetry," J. Math. Phys. 9 (7), 1072-1082 (1968).
49. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Nauka, Moscow, 1989; Pergamon, Oxford, 1982).
50. V. A. Zhelnorovich, Spinor Theory and Its Application in Physics and Mechanics (Nauka, Moscow, 1982) [in Russian].
51. D. Brill and J. Wheeler, "Interaction of Neutrinos and Gravitational Fields," Rev. Mod. Phys. 29, 465-479 (1957).
52. N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields (Nauka, Moscow, 1976; Wiley, New York, 1980).
53. P. A. M. Dirac, General Theory of Relativity (Wiley, New York, 1975; Atomizdat, Moscow, 1978).
54. G. A. Milekhin, "Nonlinear Scalar Fields and Multiple Particle Creation," Izv. Akad. Nauk SSSR, Ser. Fiz. 26, 635-641 (1962).
55. Ya. B. Zel'dovich and I. D. Novikov, Structure and Evolution of the Universe (Nauka, Moscow, 1975) [in Russian].
56. B. Saha, "Spinor Field in Bianchi Type-I Universe: Regular Solutions," Phys. Rev. D 64, 123501 (2001); gr-qc/0107013.
57. E. Kamke, Differentialgleichungen Losungsmethoden und Losungen (Akademische Verlagsgesellschaft, Leipzig, 1957).
58. V. N. Mitskevich, A. P. Efremov, and A. I. Nesterov, Dynamics of Fields in General Relativity (Energoatomizdat, Moscow, 1985) [in Russian].
59. K. A. Bronnikov and G. N. Shikin, "Cylindrically Symmetric Solitons with Nonlinear Self-Gravitating Scalar Fields," Gravit. Cosmol. 7, 231-240 (2001).
60. S. Fay, "Sufficient Conditions for Curvature Invariants to Avoid Divergences in Hyperextended Scalar-Tensor Theory for Bianchi Models," Class. Quantum. Grav. 17, 2663-2673 (2000).
61. A. L. Zel'manov and V. G. Agakov, Elements of the General Theory of Relativity (Nauka, Moscow, 1989) [in Russian].
62. N. V. Mitskievich, Physical Fields in General Relativity (Nauka, Moscow, 1969) [in Russian].
63. D. D. Rabounski and L. B. Borisova, "Particles Here and Beyond the Mirror," gr-qc/0304018.
64. A. Guth, "Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems," Phys. Rev. D 23, 347-356 (1981).
65. T. Padmanabhan, "Cosmological Constant - the Weight of the Vacuum," Phys. Rep. 38 (5-6), 235-320 (2003).
66. S. W. Hawking and R. Penrose, "The Singularities of Gravitational Collapse and Cosmology," Proc. R. Soc. Math. Phys. Sci. London 314, 529-548 (1970).
67. D. D. Ivanenko, An Attempt to construct the Unified Nonlinear Spinor Theory of Matter: Nonlinear Quantum Theory of Fields (Inostrannaya Literature, Moscow, 1959) [in Russian].
68. W. Heisenberg, Introduction to the Unifled Field Theory of Elementary Particles (Wiley, New York, 1966; Mir, Moscow, 1968).
69. B. Saha and G. N. Shikin, "Plane-Symmetric Solitons of Spinor and Scalar Fields," Czech. J. Phys. 54, 597-620 (2004).
70. H. Dicke, "Dirac's Cosmology and Mach's Principle," Nature (London) 192, 440-441 (1961).
71. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972; Mir, Moscow, 1975).
72. Y. S. Wu and Z. Wang, "Time Variation of Newton's Gravitational Constant in Superstring Theories," Phys. Rev. Lett. 57, 1978-1981 (1986).
73. K. Maeda, "On Time Variation of Fundamental Constants in Superstring Theories," Mod. Phys. Lett. A 3 (3), 243-249 (1988).
74. T. Damour, G. W. Gibbons, and J. H. Taylor, "Limits on the Variability of G Using Binary-Pulsar Data," Phys. Rev. Lett. 61 (10), 1151-1154 (1988).
75. -2," Phys. Rev. D 41, 695-698 (1990).
76. A. M. M. Abdel-Rahman, "A Critical Density Cosmological Model with Varying Gravitational and Cosmological "Constants"," Gen. Relativ. Gravit. 22, 655-663 (1990).
77. M. S. Berman, "Static Universe in a Modified Brans-Dicke Cosmology," Int. J. Theor. Phys. 29, 567-570 (1990).
78. M. S. Berman, "Kantowski-Sachs Cosmological Models with Constant Deceleration Parameter," Nuovo Cimento B 105, 239-242 (1990).
79. M. S. Berman, M. M. Som, and F. M. Gomide, "BransDicke Static Universe," Gen. Relativ. Gravit. 21, 287-292 (1989).
80. M. S. Berman and F. M. Gomide, "Cosmological Models with Constant Deceleration Parameters," Gen. Relativ. Gravit. 20, 191-198 (1988).
81. T. Singh and A. K. Agrawal, "Homogeneous Anisotropie Cosmological Models with Variable Gravitational and Cosmological Constants," Int. J. Theor. Phys. 32, 1041-1059 (1993).
82. J. A. Belinchon, "Perfect Fluid LRS Bianchi I with Time Varying Constants," gr-qc/0411005 (2004).
83. J. A. Belinchon and I. Chakrabarty, "Perfect Fluid Cosmological Models with Time-Varying Constants," Int. J. Mod. Phys. D 12, 1113-1129 (2003).
84. J. A. Belinchon and I. Chakrabarty, "Full Causal Bulk Viscous Cosmologies with Time-Varying Constants," Int. J. Mod. Phys. D 12, 861-883 (2003).
85. A. Pradhan and P. Pandey, "Plane-Symmetric Inhomogeneous Magnetized Viscous Fluid Universe with a Variable," Czech. J. Phys. 55, 749-764 (2005).
86. A. Pradhan, P. Pandey, G. P. Singh, and R. V. Deshpandey, "Causal Bulk Viscous LRS Bianchi I Models With Variable Gravitational and Cosmological "Constant"," gr-qc/03100023 (2003).
87. A. Pradhan, S. K. Srivastav, and R. S. Singh, "Tilted Bianchi Type V Bulk Viscous Cosmological Models with Varying A-Term," gr-qc/0408043 (2004).
88. K. S. Thorne, "Primordial Element Formation, Primordial Magnetic Fields, and the Isotropy of the Universe," Astrophys. J. 148, 51-68 (1967).
89. K. C. Jacobs, "Spatially Homogeneous and Euclidean Cosmological Models with Shear," Astrophys. J. 153, 661-678 (1968).
90. K. C. Jacobs, "Cosmologies of Bianchi Type I with a Uniform Magnetic Field," Astrophys. J. 155, 379-391 (1969).
91. R. Bali, "Magnetized Cosmological Model," Int. J. Theor. Phys 25, 755-761 (1986).
92. A. Lichnerowicz, Relativistic Hydrodynamics and Magnetohydrodynamics: Lectures on the Existence of Solutions (Benjamin, New York, 1967).
93. B. Saha, "Interacting Scalar and Spinor Fields in Bianchi Type I Universe Filled with Magneto-Fluid," J. Astrophys. Space Sci. 299, 149-158 (2005); gr-qc/0309062.
94. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1982; Pergamon, New York, 1988).
95. E. P. Zhidkov and I. V. Puzynin, "Solution to the Boundary Value Problems of Second Order Nonlinear Differential Equations with Stabilization Methods," Dokl. Akad. Nauk USSR 174, 271-273 (1967).
96. B. Greene, The Elegant Universe (Vintage, London, 2000).
97. B. Saha and T. Boyadjiev, "Bianchi Type-I Cosmology with Scalar and Spinor Fields," Phys. Rev. D 69, 124010 (2004).
98. B. Saha, "Anisotropic Cosmological Models with Perfect Fluid and Dark Energy," Chin. J. Phys. 43, 1035-1043 (2005); gr-qc/0412078.
99. B. Saha, "Anisotropic Cosmological Models with a Perfect fluid and a A Term," Astrophys. Space Sci. (in press); gr-qc/0411080.
100. B. Saha and V. Rikhvitsky, "Bianchi Type I Universe with Viscous Fluid: A Qualitative Analysis," gr-qc/0410056.
101. B. Saha, "Bianchi Type Universe with Viscous Fluid," Mod. Phys. Lett. A 20, 2127-2143 (2005); gr-qc/0409104.
102. B. Saha, "Nonlinear Spinor Field in Bianchi Type-I Universe Filled with Viscous Fluid: Some Special Solutions," Rom. Rep. Phys. 57, 7-24 (2005).
103. B. Saha, "Nonlinear Spinor Field in Cosmology," Phys. Rev. D 69, 124006 (2004); gr-qc/0308088.
104. B. Saha and G. N. Shikin, "Static Plane-Symmetric Nonlinear Spinor and Scalar Fields in GR," Int. J. Theor. Phys. 44, 1459 (2005).
105. M. O. Ribas, F. P. Devecchi, and G. M. Kremer, "Fermions as Sources of Accelerated Regimes in Cosmology," gr-qc/0511099.