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Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy
Інший ID:
2000 Mathematics Subject Classification: 53C60; 53C80; 83A05; 81T13; 81R40
Посилання:
Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy / G.Yu. Bogoslovsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 33 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). The author is indebted to Boris Arbuzov for informative discussion concerning the feasibility of forming the three-gluon condensate. The author is also thankful to Gary Gibbons for a helpful discussion of the status of the present-day experimental upper bounds on the space anisotropy magnitude and the prospects of the relevant fresh experiments. Finally, the author expresses his gratitude to Dimitri Pavlov and Grigori Garas’ko for the inspiring discussions that stimulated preparing the present work. Separately, the author would like to thank Hubert Goenner for many-year fruitful collaboration and also the Referees for their valuable remarks that have permitted the paper to be much improved. This work was supported in part by the Russian Foundation for Basic Research under grant RFBR-07-01-91681-RA a and by the Non-Commercial Foundation for Finsler Geometry Research.
Дата:
2008
Переглядів:
477
Завантажень:
250
Анотація:
We study the geometric phase transitions that accompany the dynamic rearrangement of vacuum under spontaneous violation of initial gauge symmetry. The rearrangement may give rise to condensates of three types, namely the scalar, axially symmetric, and entirely anisotropic condensates. The flat space-time keeps being the Minkowski space in the only case of scalar condensate. The anisotropic condensate having arisen, the respective anisotropy occurs also in space-time. In this case the space-time filled with axially symmetric condensate proves to be a flat relativistically invariant Finslerian space with partially broken 3D isotropy, while the space-time filled with entirely anisotropic condensate proves to be a flat relativistically invariant Finslerian space with entirely broken 3D isotropy. The two Finslerian space types are described briefly in the extended introduction to the work, while the original part of the latter is devoted to determining observable 3-velocities in the entirely anisotropic Finslerian event space. The main difficulties that are overcome in solving that problem arose from the nonstandard form of the light cone equation and from the necessity of correct introducing of a norm in the linear vector space of rapidities.
