Geometrical Models of the Locally Anisotropic Space-Time

Affiliation(s)

University Politehnica of Bucharest, Bucharest, Romania.

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia.

Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia.

State University of Civil Aviation, St. Petersburg, Russia.

“Transilvania” University of Bra?ov, Bra?ov, Romania.

University Politehnica of Bucharest, Bucharest, Romania.

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia.

Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia.

State University of Civil Aviation, St. Petersburg, Russia.

“Transilvania” University of Bra?ov, Bra?ov, Romania.

ABSTRACT

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

KEYWORDS

Lorentz-, Poincare- and Gauge Symmetry; Spontaneous Symmetry Breaking; Alternative Gravity Theories; Space-Time Anisotropy; Finsler Differential Geometry

Lorentz-, Poincare- and Gauge Symmetry; Spontaneous Symmetry Breaking; Alternative Gravity Theories; Space-Time Anisotropy; Finsler Differential Geometry

Cite this paper

Balan, V. , Bogoslovsky, G. , Kokarev, S. , Pavlov, D. , Siparov, S. and Voicu, N. (2012) Geometrical Models of the Locally Anisotropic Space-Time.*Journal of Modern Physics*, **3**, 1314-1335. doi: 10.4236/jmp.2012.329170.

Balan, V. , Bogoslovsky, G. , Kokarev, S. , Pavlov, D. , Siparov, S. and Voicu, N. (2012) Geometrical Models of the Locally Anisotropic Space-Time.

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[8] D. A. Kirzhnits and V. A.Chechin, “Ultra-High Energy Cosmic Rays and Possible Generalization of the Relativistic Theory,” Yadernaya Fizika, Vol. 15, No. 5, 1972, pp. 1051-1059.

[9] T. G. Pavlopoulos, “Breakdown of Lorentz Invariance,” Physical Review, Vol. 159, No. 5, 1967, pp. 1106-1110. HUdoi:10.1103/PhysRev.159.1106U

[10] S. V. Siparov, “Theory of Zero Order Effect that Can Be Used to Investigate the Space-Time Geometrical Properties,” Hypercomplex Numbers in Geometry and Physics, Vol. 3, No. 2, 2006, pp. 155-173.

[11] S. V. Siparov, “Theory of Zero Order Effect Suitable to Investigate the Space-Time Geometrical Properties,” Acta Mathematica APN, Vol. 24, No. 1, 2008, pp. 135-144.

[12] S. V. Siparov, “On the Problem of Anisotropy in Geometrodynamics,” Hypercomplex Numbers in Geometry and Physics, Vol. 5, No. 2, 2008, pp. 64-74.

[13] S. V. Siparov, “Gravitation Law and Source Model in the Anisotropic Geometrodynamics,” Hypercomplex Numbers in Geometry and Physics, Vol. 6, No. 2, 2009, pp. 140-161.

[14] S. V. Siparov, “Anisotropic Metric for the Gravitation Theory: New Ways to Interpret the Classical GRT Tests.” In: S. V. Siparov, Ed., BSG Proceedings, Geometry Balkan Press, Bucharest, 2010, pp. 205-218.

[15] S. V. Siparov, “Anisotropic Geometrodynamics in Cosmological Problems,” In: S. V. Siparov, Ed., AIP Conference Proceedings, Melville, New York, 2010, pp. 222-231.

[16] B. S. DeWitt, “Relativity, Groups and Topology,” Gordon and Breach, New York, 1964.

[17] C. Brans and R. H. Dicke, “Mach’s Principle and a Relativistic Theory of Gravitation,” Physical Review, Vol. 124, No. 3, 1961, pp. 925-935.HUdoi:10.1103/PhysRev.124.925U

[18] P. D. Mannheim and D. Kazanas, “Newtonian Limit of Conformal Gravity and the Lack of Necessity of the Second Order Poisson Equation,” General Relativity and Gravitation, Vol. 26, No. 4, 1994, pp. 337-345. HUdoi:10.1007/BF02105226U

[19] J. W. Moffat, “Nonsymmetric Gravitational Theory,” Physics Review Letters B, Vol. 355, No. 3-4, 1995, pp. 447-452. HUdoi:10.1016/0370-2693(95)00670-GU

[20] M. Milgrom, “A Modification of the Newtonian Dynam- ics as a Possible Alternative to the Hidden Mass Hypothesis,” Astrophysical Journal, Vol. 270, 1983, pp. 365- 370. HUdoi:10.1086/161130U

[21] J. D. Bekenstein, “Relativistic Gravitation Theory for the Modified Newtonian Dynamics Paradigm,” Physics Review D, Vol. 70, No. 8, 2004, pp. 1-28.

[22] J. Lense and H. Thirring, “On the Influence of the Proper Rotation of Central Bodies on the Motions of Planets and Moons According to Einstein’s Theory of Gravitation,” Physikalische Zeitschrift/Physical Journal, Vol. 19, 1918, pp. 156- 163.

[23] M. L. Ruggiero and A. Tartaglia, “Gravitomagnetic Effects,” Preprint, 2002. arXiv:gr-qc/0207065v2

[24] H. Muller, S. W. Chiow, S. Herrmann, S. Chu and K. Y. Chung, “Atom Interferometry Tests of the Isotropy of Post-Newtonian Gravity,” Physics Review Letters, Vol. 100, No. 3, 2008, pp. 1-4.

[25] The CMS Collaboration, “Observation of Long-Range Near-Side Angular Correlations in Proton-Proton Collisions at the LHC,” JHEP, Vol. 9, 2010, pp. 1-37;.

[26] D. Colladay and V. A. Kostelecky, “Lorentz-Violating Extension of the Standard Model,” Physics Review D, Vol. 58, No. 11, 1998, pp. 1-23.

[27] Q. G. Bailey and A. Kostelecky, “Signals for Lorentz Violation in Post-Newtonian Gravity,” Physics Review D, Vol. 74, No. 4, 2006, pp. 1-46.

[28] V. A. Kostelecky, “CPT and Lorentz Symmetry,” World Scientific, Singapore, 1999.

[29] V. A. Kostelecky, “CPT and Lorentz Symmetry II,” World Scientific, Singapore, 2002.

[30] V. A. Kostelecky, “CPT and Lorentz Symmetry III,” World Scientific, Singapore, 2005.

[31] V. A. Kostelecky, “CPT and Lorentz Symmetry IV,” World Scientific, Singapore, 2008.

[32] V. A. Kostelecky, “CPT and Lorentz Symmetry V,” World Scientific, Singapore, 2011.

[33] D. Blas and S. Sibiryakov, “Technically Natural Dark Energy from Lorentz Breaking,” Preprint, 2011. arXiv:1104.3579v1 [hep-th]

[34] G. Yu. Bogoslovsky and H. F. Goenner, “Finslerian Spaces Possessing Local Relativistic Symmetry,” General Rela- tivity and Gravitation, Vol. 31, No. 10, 1999, pp. 1565-1603. HUdoi:10.1023/A:1026786505326U

[35] J. Patera, P. Winternitz and H. Zassenhaus, “Continuous Subgroups of the Fundamental Groups of Physics. II. The Similitude Group,” Journal of Mathematical Physics, Vol. 16, No. 8, 1975, pp. 1615-1624. HUdoi:10.1063/1.522730U

[36] P. Winternitz and I. Fris, “Invariant Expansions of Relativistic Amplitudes and Subgroups of the Proper Lorentz Group,” Yadernaya Fizika, Vol. 1, No. 5, 1965, pp. 889- 901.

[37] G. Yu. Bogoslovsky, “Lorentz Symmetry Violation without Violation of Relativistic Symmetry,” Physics Letters A, Vol. 350, No. 1-2, 2006, pp. 5-10. HUdoi:10.1016/j.physleta.2005.11.007U

[38] A. G. Cohen and S. L. Glashow, “Very Special Relativity,” Physics Review Letters, Vol. 97, No. 2, 2006, pp. 1- 3.

[39] A. G. Cohen and S. L. Glashow, “A Lorentz-Violating Origin of Neutrino Mass?” Preprint, 2006. arXiv:hep-ph/0605036v1.

[40] G. W. Gibbons, J. Gomis and C. N. Pope, “General Very Special Relativity is Finsler Geometry,” Physics Review D, Vol. 76, No. 8, 2007, pp. 1-5.

[41] G. W. Gibbons, J. Gomis and C. N. Pope, “Deforming the Maxwell-Sim Algebra,” Physics Review D, Vol. 82, No. 6, 2010, pp. 1-15.

[42] G. Yu. Bogoslovsky and H. F. Goenner, “Concerning the Generalized Lorentz Symmetry and the Generalization of the Dirac Equation,” Physics Letters A, Vol. 323, No. 1-2, 2004, pp. 40-47. HUdoi:10.1016/j.physleta.2004.01.040U

[43] G. Yu. Bogoslovsky, “Some Physical Displays of the Space Anisotropy Relevant to the Feasibility of Its Being Detected at a Laboratory,” Preprint, 2007. arXiv:0706.2621v1 [gr-qc]

[44] G. Yu. Bogoslovsky, “Finsler Model of Space-Time,” Physics of Particles and Nuclei, Vol. 24, No. 3, 1993, pp. 354-379.

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